What is the integral of x^2e^{3x} ?

The integral of x^2e^{3x} is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^2e^{3x}

\int x^{2} e^{3 x} d x

\frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

Solution steps

\int x^{2} e^{3 x} d x

Apply Integration By Parts

= \frac{1}{3} e^{3 x} x^{2} - \int \frac{2}{3} e^{3 x} x d x

\int \frac{2}{3} e^{3 x} x d x = \frac{2}{27} (3 e^{3 x} x - e^{3 x})

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x})

Add a constant to the solution

= \frac{1}{3} e^{3 x} x^{2} - \frac{2}{27} (3 e^{3 x} x - e^{3 x}) + C

What is the integral of x^2e^{3x} ?
The integral of x^2e^{3x} is 1/3 e^{3x}x^2-2/27 (3e^{3x}x-e^{3x})+C