Which integral is ${\int }_4^{16}\frac{e^{\sqrt{x}}}{\sqrt{x}}dx$ after the substitution $u=\sqrt{x}$?

Evaluate ${\int }_0^{2}x{\left(x^2+5\right)}^{2}dx$.

Evaluate ${\int }_0^{3}x{e}^{x^2}dx$.

Which integral is ${\int }_0^{1}x{\left(x^2+5\right)}^{3}dx$ after the substitution $u=x^2+5$?

Which integral is ${\int }_0^{2}x{\left(x^2+3\right)}^{2}dx$ after the substitution $u=x^2+3$?

Evaluate ${\int }_0^{2}x{\left(x^2+4\right)}^{3}dx$.

Evaluate ${\int }_0^2\frac{1}{4x+1}dx$.

Which integral is ${\int }_1^9\frac{e^{\sqrt{x}}}{\sqrt{x}}dx$ after the substitution $u=\sqrt{x}$?

Evaluate ${\int }_0^2\frac{1}{2x+1}dx$.

Evaluate ${\int }_0^{2}x{\left(x^2+2\right)}^{2}dx$.

Evaluate ${\int }_0^{\frac{\pi }{2}}\sin x{\cos }^{4}xdx$, with $x$ in radians.

Evaluate ${\int }_0^{\frac{\pi }{2}}\sin x{\cos }^{6}xdx$, with $x$ in radians.

Evaluate ${\int }_{-3}^{3}x{\left(x^2+1\right)}^{3}dx$.

Evaluate ${\int }_0^{1}x{\left(x^2+2\right)}^{3}dx$.

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

A student evaluates ${\int }_0^{1}2x{\left(x^2+3\right)}^{2}dx$ like this: $u=x^2+3$, $du=2xdx$, so the integral is ${\int }_0^1{u}^{2}du=\frac{1}{3}$. What went wrong?

Evaluate ${\int }_0^{\frac{\pi }{2}}\cos x{\sin }^{3}xdx$, with $x$ in radians.

Evaluate ${\int }_0^3\frac{1}{3x+1}dx$.

Evaluate ${\int }_0^4\frac{1}{5x+1}dx$.

Evaluate ${\int }_0^{1}x{\left(x^2+4\right)}^{2}dx$.

Evaluate ${\int }_0^{2}x{\left(x^2+3\right)}^{3}dx$.

Evaluate ${\int }_0^{2}x{\left(x^2+3\right)}^{2}dx$.

A student evaluates ${\int }_0^{1}2x{\left(x^2+1\right)}^{2}dx$ like this: $u=x^2+1$, $du=2xdx$, so the integral is ${\int }_0^1{u}^{2}du=\frac{1}{3}$. What went wrong?

Which integral is ${\int }_0^{2}x{\left(x^2+5\right)}^{3}dx$ after the substitution $u=x^2+5$?

Evaluate ${\int }_0^3\frac{1}{2x+1}dx$.

Evaluate ${\int }_0^{\frac{\pi }{4}}{\sec }^{2}x\tan xdx$, with $x$ in radians.

Evaluate ${\int }_0^{\frac{\pi }{2}}\cos x\sin xdx$, with $x$ in radians.

Evaluate ${\int }_0^{\frac{\pi }{4}}{\sec }^{2}x{\tan }^{4}xdx$, with $x$ in radians.

A student evaluates ${\int }_0^{1}2x{\left(x^2+4\right)}^{3}dx$ like this: $u=x^2+4$, $du=2xdx$, so the integral is ${\int }_0^1{u}^{3}du=\frac{1}{4}$. What went wrong?

Evaluate ${\int }_0^{1}x{\left(x^2+1\right)}^{2}dx$.