Find $\int x\sqrt{x-1}dx$.

Find $\int {\tan }^{4}x{\sec }^{2}xdx$, with $x$ in radians.

A student evaluates $\int 4x^3{e}^{x^4+2}dx$ like this: let $u=x^4+2$, so $du=4x^{3}dx$ and the integral is $\int e^{u}du=e^u+C$. Is the work correct?

Find $\int \frac{4x^3}{x^4+9}dx$.

Find $\int x{\left(x^2+8\right)}^{3}dx$.

In $\int {\sec }^2\left(2x\right)dx$ with $u=2x$, what does the integral become?

Find $\int -x^2{e}^{x^3}dx$.

For $\int x^3{\left(x^4+5\right)}^{2}dx$, which substitution turns the integral into one in $u$ alone?

Find $\int \frac{2x}{x^2+8}dx$.

For $\int x{\left(x^2+2\right)}^{3}dx$, which substitution turns the integral into one in $u$ alone?

In $\int e^{3x}dx$ with $u=3x$, what does the integral become?

Find $\int x{\left(x^2+4\right)}^{3}dx$.

For $\int x{\left(x^2+6\right)}^{6}dx$, which substitution turns the integral into one in $u$ alone?

Find $\int x{\left(x^2+3\right)}^{4}dx$.

Find $\int x{\left(x^2+1\right)}^{5}dx$.

For $\int x{\left(x^2+6\right)}^{4}dx$, which substitution turns the integral into one in $u$ alone?

Find $\int {\tan }^{3}x{\sec }^{2}xdx$, with $x$ in radians.

Find $\int -2x{e}^{x^2}dx$.

Find $\int {\tan }^{2}x{\sec }^{2}xdx$, with $x$ in radians.

For $\int x^2\sqrt{x^3+6}dx$, which substitution turns the integral into one in $u$ alone?

Find $\int {\cos }^{5}x\sin xdx$, with $x$ in radians.

In $\int {\sec }^2\left(4x\right)dx$ with $u=4x$, what does the integral become?

Find $\int x{\left(x^2+4\right)}^{5}dx$.

In $\int e^{8x}dx$ with $u=8x$, what does the integral become?

Find $\int {\cos }^{4}x\sin xdx$, with $x$ in radians.

A student evaluates $\int x^3{e}^{x^4+8}dx$ like this: let $u=x^4+8$, so $du=x^{3}dx$ and the integral is $\int e^{u}du=e^{x^4+8}+C$. Is the work correct?

Find $\int x\sqrt{x-4}dx$.

Find $\int x{\left(x^2+8\right)}^{5}dx$.

Find $\int x\sqrt{x-8}dx$.

Find $\int -3x^3{e}^{x^4}dx$.

In $\int {\sec }^2\left(8x\right)dx$ with $u=8x$, what does the integral become?

Find $\int {\sin }^{3}x\cos xdx$, with $x$ in radians.

Find $\int x{\left(x^2+1\right)}^{6}dx$.

Find $\int 2x^2{e}^{x^3}dx$.

In $\int {\sec }^2\left(6x\right)dx$ with $u=6x$, what does the integral become?

Find $\int x{\left(x^2+4\right)}^{6}dx$.

Find $\int {\cos }^{2}x\sin xdx$, with $x$ in radians.

Find $\int 3x{e}^{x^2}dx$.

For $\int x^3{\left(x^4+9\right)}^{2}dx$, which substitution turns the integral into one in $u$ alone?

A student evaluates $\int 2x{e}^{x^2+4}dx$ like this: let $u=x^2+4$, so $du=2xdx$ and the integral is $\int e^{u}du=e^u+C=e^{x^2+4}+C$. Is the work correct?