What is the integral of xe^{(x^2)/5} ?

The integral of xe^{(x^2)/5} is 5/2 e^{(x^2)/5}+C

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integral of xe^{(x^2)/5}

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

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

Solution steps

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

Apply u-substitution

: \int \frac{e ^{\frac{u}{5}}}{2} d u

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

Apply u-substitution

: \int e^{v} \cdot 5 d v

= \frac{1}{2} \cdot \int e^{v} \cdot 5 d v

Take the constant out:

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

= \frac{1}{2} \cdot 5 \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{2} \cdot 5 e^{v}

Substitute back

= \frac{1}{2} \cdot 5 e^{\frac{x ^{2}}{5}}

Simplify

\frac{1}{2} \cdot 5 e^{\frac{x ^{2}}{5}} : \frac{5}{2} e^{\frac{x ^{2}}{5}}

= \frac{5}{2} e^{\frac{x ^{2}}{5}}

Add a constant to the solution

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

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