What is the integral of x^3e^{x^6} ?

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integral of x^3e^{x^6}

\int x^{3} e^{x^{6}} d x

Solution steps

\int x^{3} e^{x^{6}} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{e ^{v^{\frac{3}{2}}}}{2} d v

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

Take the constant out:

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

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

Use the nonelementary integral:

Substitute back

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