What is the integral of xe^{8x^2} ?

The integral of xe^{8x^2} is 1/16 e^{8x^2}+C

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integral of xe^{8x^2}

\int x e^{8 x^{2}} d x

\frac{1}{16} e^{8 x^{2}} + C

Solution steps

\int x e^{8 x^{2}} d x

Apply u-substitution

: \int \frac{e ^{u}}{16} d u

= \int \frac{e ^{u}}{16} d u

Take the constant out:

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

= \frac{1}{16} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{16} e^{u}

Substitute back

u = 8 x^{2}

= \frac{1}{16} e^{8 x^{2}}

Add a constant to the solution

= \frac{1}{16} e^{8 x^{2}} + C

\frac{d y}{d t} = e^{t} (1 - 1)^{2}

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f (x) = \frac{( x ^{2} + 1 )}{x - 1}

\int (7^{x}) d x

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

What is the integral of xe^{8x^2} ?
The integral of xe^{8x^2} is 1/16 e^{8x^2}+C