What is the integral of (3x-2)e-x ?

The integral of (3x-2)e-x is e((3x^2)/2-2x)-(x^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x-2)e-x

\int (3 x - 2) e - x d x

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

Solution steps

\int (3 x - 2) e - x 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 (3 x - 2) e d x - \int x d x

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

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

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

Add a constant to the solution

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

f^{^{'}} (x) = 5 e^{x} + 3 x^{2} - 2 x

\frac{\partial}{\partial x} (x^{2} + x y^{2})

\int \frac{1}{6 x ( 5 + x )} d x

6 y^{^{''}} + 31 y = 0

x \to 4 lim (\frac{x ^{3} - 6}{x - 4})

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