What is the integral of xe^{2/5 x^2+7} ?

The integral of xe^{2/5 x^2+7} is 5/4 e^{2/5 x^2+7}+C

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integral of xe^{2/5 x^2+7}

\int x e^{\frac{2}{5} x^{2} + 7} d x

\frac{5}{4} e^{\frac{2}{5} x^{2} + 7} + C

Solution steps

\int x e^{\frac{2}{5} x^{2} + 7} d x

Apply u-substitution

: \int \frac{5 e ^{u}}{4} d u

= \int \frac{5 e ^{u}}{4} d u

Take the constant out:

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

= \frac{5}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{5}{4} e^{u}

Substitute back

u = \frac{2}{5} x^{2} + 7

= \frac{5}{4} e^{\frac{2}{5} x^{2} + 7}

Add a constant to the solution

= \frac{5}{4} e^{\frac{2}{5} x^{2} + 7} + C

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What is the integral of xe^{2/5 x^2+7} ?
The integral of xe^{2/5 x^2+7} is 5/4 e^{2/5 x^2+7}+C