What is the integral of xe^{(x^2)/4} ?

The integral of xe^{(x^2)/4} is 2e^{(x^2)/4}+C

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integral of xe^{(x^2)/4}

\int x e^{\frac{x ^{2}}{4}} d x

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

Solution steps

\int x e^{\frac{x ^{2}}{4}} d x

Apply u-substitution

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

Apply u-substitution

= \frac{1}{2} \cdot \int e^{v} \cdot 4 d v

Take the constant out:

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

= \frac{1}{2} \cdot 4 \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{2} \cdot 4 e^{v}

Substitute back

= \frac{1}{2} \cdot 4 e^{\frac{x ^{2}}{4}}

Simplify

\frac{1}{2} \cdot 4 e^{\frac{x ^{2}}{4}} : 2 e^{\frac{x ^{2}}{4}}

= 2 e^{\frac{x ^{2}}{4}}

Add a constant to the solution

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

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