What is the integral of x*e^{1-x^2} ?

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

integral of x*e^{1-x^2}

\int x \cdot e^{1 - x^{2}} d x

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

Solution steps

\int x e^{1 - x^{2}} d x

Apply u-substitution

= \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 = 1 - x^{2}

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

Add a constant to the solution

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

\int \frac{( e ^{x} + 1 ) ^{2}}{e ^{x}} d x

\frac{d}{d x} (\frac{1}{27} (2 x - 1)^{3} (6 - 3 x) + 1)

\int_{0}^{\frac{π}{4}} sin (4 x) d x

in v erse l a pl a ce \frac{- 3}{( s - 1 ) ^{2}}

d er i v a t i v e f (x) = \frac{x ^{3}}{3} + 4 x^{2} + 12 x + 19

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