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

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

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integral of xe^{8-x^2}

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

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

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

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

= - \frac{1}{2} e^{u}

Substitute back

u = 8 - x^{2}

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

Add a constant to the solution

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

\int \frac{8}{x} - \frac{5}{x ^{2}} + \frac{6}{x ^{3}} d x

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

\int \frac{ln ^{8} ( z )}{z} d z

\int (3 x^{2} ln (4 x) + x^{2}) d x

\int \frac{3 x ^{2} + 1}{x ^{2} - 1} d x

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