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Popular >

integral of+xe-x^2

Solution

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

Solution

\frac{e x ^{2}}{2} - \frac{x ^{3}}{3} + C

Solution steps

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

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

= \frac{e x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

= \frac{e x ^{2}}{2} - \frac{x ^{3}}{3} + C

Popular Examples

integral of (3x^2+5x+4)/(x^3+x^2+x-3)

\int \frac{3 x ^{2} + 5 x + 4}{x ^{3} + x ^{2} + x - 3} d x

integral of (9x)/(sqrt(2+15x))

\int \frac{9 x}{2 + 15 x} d x

integral of sin(1-2x)sin(2x+3)

\int sin (1 - 2 x) sin (2 x + 3) d x

integral of (3x^3-x)(2-x)

\int (3 x^{3} - x) (2 - x) d x

integral of ((y+4))/(y^2+16)

\int \frac{( y + 4 )}{y ^{2} + 16} d y

Frequently Asked Questions (FAQ)

What is the integral of+xe-x^2 ?
The integral of+xe-x^2 is (ex^2)/2-(x^3)/3+C