What is the integral of (x^2-5x)e^x ?

The integral of (x^2-5x)e^x is e^xx^2-7e^xx+7e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2-5x)e^x

integral

(x^{2} - 5 x) e^{x}

e^{x} x^{2} - 7 e^{x} x + 7 e^{x} + C

Solution steps

\int (x^{2} - 5 x) e^{x} d x

Apply Integration By Parts

: (x^{2} - 5 x) e^{x} - \int (2 x - 5) e^{x} d x

= (x^{2} - 5 x) e^{x} - \int (2 x - 5) e^{x} d x

\int (2 x - 5) e^{x} d x = 2 e^{x} x - 7 e^{x}

= (x^{2} - 5 x) e^{x} - (2 e^{x} x - 7 e^{x})

Simplify

(x^{2} - 5 x) e^{x} - (2 e^{x} x - 7 e^{x}) : e^{x} x^{2} - 7 e^{x} x + 7 e^{x}

= e^{x} x^{2} - 7 e^{x} x + 7 e^{x}

Add a constant to the solution

= e^{x} x^{2} - 7 e^{x} x + 7 e^{x} + C

\frac{( x + 3 )}{( x ^{2} + 3 )}

\frac{1}{cos ^{2} ( y )}

\frac{x ^{2}}{x}

3 - 5 x^{2}

\frac{2 sin ( x )}{( 5 + 3 cos ( x ) )}

What is the integral of (x^2-5x)e^x ?
The integral of (x^2-5x)e^x is e^xx^2-7e^xx+7e^x+C