What is the integral of x*e^{ax} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x*e^{ax}

\int x \cdot e^{a x} d x

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

Solution steps

\int x e^{a x} d x

Apply Integration By Parts

: e^{a x} \frac{1}{a} x - \int e^{a x} \frac{1}{a} d x

= e^{a x} \frac{1}{a} x - \int e^{a x} \frac{1}{a} d x

\int e^{a x} \frac{1}{a} d x = e^{a x} \frac{1}{a ^{2}}

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

Add a constant to the solution

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

\int x d x

\int (5 x) d x

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

\int e^{x + 6} d x

\int z z - 9 d z

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