What is the integral of (y^2e^{y^3})/2 ?

The integral of (y^2e^{y^3})/2 is 1/6 e^{y^3}+C

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integral of (y^2e^{y^3})/2

\int \frac{y ^{2} e ^{y^{3}}}{2} d y

\frac{1}{6} e^{y^{3}} + C

Solution steps

\int \frac{y ^{2} e ^{y^{3}}}{2} d y

Take the constant out:

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

= \frac{1}{2} \cdot \int y^{2} e^{y^{3}} d y

Apply u-substitution

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

= \frac{1}{2} \cdot \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}{2} \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{2} \cdot \frac{1}{3} e^{u}

Substitute back

u = y^{3}

= \frac{1}{2} \cdot \frac{1}{3} e^{y^{3}}

Simplify

\frac{1}{2} \cdot \frac{1}{3} e^{y^{3}} : \frac{1}{6} e^{y^{3}}

= \frac{1}{6} e^{y^{3}}

Add a constant to the solution

= \frac{1}{6} e^{y^{3}} + C

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What is the integral of (y^2e^{y^3})/2 ?
The integral of (y^2e^{y^3})/2 is 1/6 e^{y^3}+C