What is the integral of x^2xe^{x^2} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2xe^{x^2}

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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