What is the integral of p^2e^{p^3} ?

The integral of p^2e^{p^3} is 1/3 e^{p^3}+C

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integral of p^2e^{p^3}

\int p^{2} e^{p^{3}} d p

\frac{1}{3} e^{p^{3}} + C

Solution steps

\int p^{2} e^{p^{3}} d p

Apply u-substitution

: \int \frac{e ^{u^{\frac{3}{2}}} u}{2 p} d u

= \int \frac{e ^{u}}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= \frac{1}{3} e^{u}

Substitute back

u = p^{3}

= \frac{1}{3} e^{p^{3}}

Add a constant to the solution

= \frac{1}{3} e^{p^{3}} + C

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What is the integral of p^2e^{p^3} ?
The integral of p^2e^{p^3} is 1/3 e^{p^3}+C