What is the integral of 32x*e^{8x^2} ?

The integral of 32x*e^{8x^2} is 2e^{8x^2}+C

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integral of 32x*e^{8x^2}

\int 32 x \cdot e^{8 x^{2}} d x

2 e^{8 x^{2}} + C

Solution steps

\int 32 x e^{8 x^{2}} d x

Take the constant out:

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

= 32 \cdot \int x e^{8 x^{2}} d x

Apply u-substitution

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

= 32 \cdot \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

= 32 \cdot \frac{1}{16} \cdot \int e^{u} d u

Use the common integral:

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

= 32 \cdot \frac{1}{16} e^{u}

Substitute back

u = 8 x^{2}

= 32 \cdot \frac{1}{16} e^{8 x^{2}}

Simplify

32 \cdot \frac{1}{16} e^{8 x^{2}} : 2 e^{8 x^{2}}

= 2 e^{8 x^{2}}

Add a constant to the solution

= 2 e^{8 x^{2}} + C

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What is the integral of 32x*e^{8x^2} ?
The integral of 32x*e^{8x^2} is 2e^{8x^2}+C