Choosing an Integration Technique

Question 1

Find (^2 x - 3x^5) \, dx, with x in radians.

Accepted Answer

x - 12x^6 + C

Answer

^3 x3 - 12x^6 + C

Answer

x - 15x^4 + C

Answer

12x - 12x^6 + C

Question 2

Find (^2 x + 7x^3) \, dx, with x in radians.

Accepted Answer

x + 74x^4 + C

Answer

^3 x3 + 74x^4 + C

Answer

x + 21x^2 + C

Answer

12x + 74x^4 + C

Question 3

Find x(x^2 + 2)^6 \, dx.

Accepted Answer

(x^2 + 2)^714 + C

Answer

(x^2 + 2)^77 + C

Answer

x^2(x^2 + 2)^714 + C

Answer

12x(x^2 + 2)^5 + C

Question 4

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

xe^x^2 \, dx substitutes with u = x^2, while e^x^2 \, dx has no factor to supply du

Answer

Both substitute with u = x^2

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

e^x^2 \, dx = e^x^22x + C, by dividing by the derivative of the inner function

Question 5

Which technique does 2x^3 - xx^2 \, dx call for?

Accepted Answer

An algebraic rewrite first, then a direct antiderivative

Answer

A u-substitution

Answer

A direct antiderivative, with no substitution

Answer

None of these: the power rule cannot reach this integrand

Question 6

Find 6xe^x^2 \, dx.

Accepted Answer

6e^x^22 + C

Answer

12e^x^2 + C

Answer

6e^x^2 + C

Answer

6e^x^22x + C

Question 7

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

x(x^2) \, dx substitutes with u = x^2, while (x^2) \, dx has no factor to supply du

Answer

Both substitute with u = x^2

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

(x^2) \, dx = (x^2)2x + C, by dividing by the derivative of the inner function

Question 8

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

xx \, dx substitutes with u = x, while (x^2) \, dx has no factor to supply du

Answer

Both substitute with u = x

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

(x^2) \, dx = (x^2)x + C, by dividing by the derivative of the inner function

Question 9

Which technique does x^2 + 4xx \, dx call for?

Accepted Answer

An algebraic rewrite first, then a direct antiderivative

Answer

A u-substitution

Answer

A direct antiderivative, with no substitution

Answer

None of these: the power rule cannot reach this integrand

Question 10

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

xx \, dx substitutes with u = x, while x \, dx has no factor to supply du

Answer

Both substitute with u = x

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

x \, dx = x1x + C, by dividing by the derivative of the inner function

Question 11

Find 2xx^2 + 4 \, dx.

Accepted Answer

(x^2 + 4) + C

Answer

2x(x^2 + 4) + C

Answer

x^2(x^2 + 4) + C

Answer

12(x^2 + 4) + C

Question 12

Find (^2 x + 5x^5) \, dx, with x in radians.

Accepted Answer

x + 56x^6 + C

Answer

^3 x3 + 56x^6 + C

Answer

x + 25x^4 + C

Answer

12x + 56x^6 + C

Question 13

Find -3x^3 - 8xx^2 \, dx.

Accepted Answer

-32x^2 - 8| x | + C

Answer

-32x^2 + 8| x | + C

Answer

-34x^4 - 4x^2x^33 + C

Answer

(-3x^3 - 8x)^22x^2 + C

Question 14

Find (^2 x + 9x^6) \, dx, with x in radians.

Accepted Answer

x + 97x^7 + C

Answer

^3 x3 + 97x^7 + C

Answer

x + 54x^5 + C

Answer

12x + 97x^7 + C

Question 15

Find (^2 x + 5x^3) \, dx, with x in radians.

Accepted Answer

x + 54x^4 + C

Answer

^3 x3 + 54x^4 + C

Answer

x + 15x^2 + C

Answer

12x + 54x^4 + C

Question 16

Find -2x^3 - 4xx^2 \, dx.

Accepted Answer

-x^2 - 4| x | + C

Answer

-x^2 + 4| x | + C

Answer

-12x^4 - 2x^2x^33 + C

Answer

(-2x^3 - 4x)^22x^2 + C

Question 17

Which technique does (x + e^x) \, dx call for?

Accepted Answer

A direct antiderivative, with no substitution

Answer

A u-substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Answer

None of these: the power rule cannot reach this integrand

Question 18

Find 4x^3x^4 + 1 \, dx.

Accepted Answer

(x^4 + 1) + C

Answer

4x^3(x^4 + 1) + C

Answer

x^4(x^4 + 1) + C

Answer

14(x^4 + 1) + C

Question 19

Which technique does (x)^2x \, dx call for?

Accepted Answer

A u-substitution

Answer

A direct antiderivative, with no substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Answer

None of these: the power rule cannot reach this integrand

Question 20

Which technique does (^2 x - 4x^3) \, dx call for?

Accepted Answer

A direct antiderivative, with no substitution

Answer

A u-substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Answer

None of these: the power rule cannot reach this integrand

Question 21

Which technique does x^2 + 9 \, dx call for?

Accepted Answer

None of these: the power rule cannot reach this integrand

Answer

A u-substitution

Answer

A direct antiderivative, with no substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Question 22

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

x^2x^3 + 1 \, dx substitutes with u = x^3 + 1, while x^3 + 1 \, dx has no factor to supply du

Answer

Both substitute with u = x^3 + 1

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

x^3 + 1 \, dx = x^3 + 13x^2 + C, by dividing by the derivative of the inner function

Question 23

Find x^3 - 9xx^2 \, dx.

Accepted Answer

12x^2 - 9| x | + C

Answer

12x^2 + 9| x | + C

Answer

14x^4 - 92x^2x^33 + C

Answer

(x^3 - 9x)^22x^2 + C

Question 24

Which technique does xx^2 + 4 \, dx call for?

Accepted Answer

A u-substitution

Answer

A direct antiderivative, with no substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Answer

None of these: the power rule cannot reach this integrand

Question 25

Find (^2 x + 5x^6) \, dx, with x in radians.

Accepted Answer

x + 57x^7 + C

Answer

^3 x3 + 57x^7 + C

Answer

x + 30x^5 + C

Answer

12x + 57x^7 + C

Question 26

Find x(x^2 + 7)^3 \, dx.

Accepted Answer

(x^2 + 7)^48 + C

Answer

(x^2 + 7)^44 + C

Answer

x^2(x^2 + 7)^48 + C

Answer

6x(x^2 + 7)^2 + C

Question 27

Find (^2 x - 7x^6) \, dx, with x in radians.

Accepted Answer

x - x^7 + C

Answer

^3 x3 - x^7 + C

Answer

x - 42x^5 + C

Answer

12x - x^7 + C

Question 28

Find (^2 x - 3x^6) \, dx, with x in radians.

Accepted Answer

x - 37x^7 + C

Answer

^3 x3 - 37x^7 + C

Answer

x - 18x^5 + C

Answer

12x - 37x^7 + C

Question 29

Find x(x^2 + 7)^5 \, dx.

Accepted Answer

(x^2 + 7)^612 + C

Answer

(x^2 + 7)^66 + C

Answer

x^2(x^2 + 7)^612 + C

Answer

10x(x^2 + 7)^4 + C

Question 30

One of these two integrals can be done by a u-substitution and the other cannot. Which statement is correct?

Accepted Answer

2xx^2 + 1 \, dx substitutes with u = x^2 + 1, while 1x^2 + 1 \, dx has no factor to supply du

Answer

Both substitute with u = x^2 + 1

Answer

Neither substitutes, because the integrand is a composite in each case

Answer

1x^2 + 1 \, dx = 1x^2 + 12x + C, by dividing by the derivative of the inner function

Question 31

Find -x^3e^x^4 \, dx.

Accepted Answer

-e^x^44 + C

Answer

-4e^x^4 + C

Answer

-e^x^4 + C

Answer

-e^x^44x^3 + C

Question 32

Find 8x^3 - xx^2 \, dx.

Accepted Answer

4x^2 - | x | + C

Answer

4x^2 + | x | + C

Answer

2x^4 - 12x^2x^33 + C

Answer

(8x^3 - x)^22x^2 + C

Question 33

Which technique does 1x^2 + 1 \, dx call for?

Accepted Answer

A direct antiderivative, with no substitution

Answer

A u-substitution

Answer

An algebraic rewrite first, then a direct antiderivative

Answer

None of these: the power rule cannot reach this integrand

Question 34

Find 3x^3 - xx^2 \, dx.

Accepted Answer

32x^2 - | x | + C

Answer

32x^2 + | x | + C

Answer

34x^4 - 12x^2x^33 + C

Answer

(3x^3 - x)^22x^2 + C

Question 35

Find 3x^3 - 5xx^2 \, dx.

Accepted Answer

32x^2 - 5| x | + C

Answer

32x^2 + 5| x | + C

Answer

34x^4 - 52x^2x^33 + C

Answer

(3x^3 - 5x)^22x^2 + C

Question 36

Find x(x^2 + 9)^2 \, dx.

Accepted Answer

(x^2 + 9)^36 + C

Answer

(x^2 + 9)^33 + C

Answer

x^2(x^2 + 9)^36 + C

Answer

4x(x^2 + 9) + C

Question 37

Find x(x^2 + 9)^4 \, dx.

Accepted Answer

(x^2 + 9)^510 + C

Answer

(x^2 + 9)^55 + C

Answer

x^2(x^2 + 9)^510 + C

Answer

8x(x^2 + 9)^3 + C

Question 38

Find 5x^3 - 3xx^2 \, dx.

Accepted Answer

52x^2 - 3| x | + C

Answer

52x^2 + 3| x | + C

Answer

54x^4 - 32x^2x^33 + C

Answer

(5x^3 - 3x)^22x^2 + C

Question 39

Find 2x^3 - 8xx^2 \, dx.

Accepted Answer

x^2 - 8| x | + C

Answer

x^2 + 8| x | + C

Answer

12x^4 - 4x^2x^33 + C

Answer

(2x^3 - 8x)^22x^2 + C

Question 40

Find -4x^3 - 7xx^2 \, dx.

Accepted Answer

-2x^2 - 7| x | + C

Answer

-2x^2 + 7| x | + C

Answer

-x^4 - 72x^2x^33 + C

Answer

(-4x^3 - 7x)^22x^2 + C

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Choosing an Integration Technique

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Choosing an Integration Technique

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner