What is the integral of xe^{2x^3} ?

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integral of xe^{2x^3}

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

Solution steps

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

Apply u-substitution

Take the constant out:

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

Apply u-substitution

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

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the nonelementary integral:

Substitute back

Add a constant to the solution