What is the integral of x*e^{2x^2} ?

The integral of x*e^{2x^2} is 1/4 e^{2x^2}+C

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integral of x*e^{2x^2}

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

\frac{1}{4} e^{2 x^{2}} + C

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 2 x^{2}

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

Add a constant to the solution

= \frac{1}{4} e^{2 x^{2}} + C

y = \frac{x}{x + 5}

\int_{1}^{2} - x^{2} + 3 x - 2 d x

2 x^{2} \frac{d y}{d x} + 2 x y = y^{3}

\int 36 - 9 x^{2} d x

\frac{d}{d s} (\frac{1 - s ^{2}}{( s ^{2} + 1 ) ^{2}})

What is the integral of x*e^{2x^2} ?
The integral of x*e^{2x^2} is 1/4 e^{2x^2}+C