What is the integral of x^2e^{7x} ?

The integral of x^2e^{7x} is 1/7 e^{7x}x^2-2/343 (7e^{7x}x-e^{7x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2e^{7x}

\int x^{2} e^{7 x} d x

\frac{1}{7} e^{7 x} x^{2} - \frac{2}{343} (7 e^{7 x} x - e^{7 x}) + C

Solution steps

\int x^{2} e^{7 x} d x

Apply Integration By Parts

= \frac{1}{7} e^{7 x} x^{2} - \int \frac{2}{7} e^{7 x} x d x

\int \frac{2}{7} e^{7 x} x d x = \frac{2}{343} (7 e^{7 x} x - e^{7 x})

= \frac{1}{7} e^{7 x} x^{2} - \frac{2}{343} (7 e^{7 x} x - e^{7 x})

Add a constant to the solution

= \frac{1}{7} e^{7 x} x^{2} - \frac{2}{343} (7 e^{7 x} x - e^{7 x}) + C

What is the integral of x^2e^{7x} ?
The integral of x^2e^{7x} is 1/7 e^{7x}x^2-2/343 (7e^{7x}x-e^{7x})+C