What is the integral of e^{6x}x^2 ?

The integral of e^{6x}x^2 is 1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{6x}x^2

\int e^{6 x} x^{2} d x

\frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}) + C

Solution steps

\int e^{6 x} x^{2} d x

Apply Integration By Parts

: \frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x

= \frac{1}{6} e^{6 x} x^{2} - \int \frac{1}{3} e^{6 x} x d x

\int \frac{1}{3} e^{6 x} x d x = \frac{1}{108} (6 e^{6 x} x - e^{6 x})

= \frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x})

Add a constant to the solution

= \frac{1}{6} e^{6 x} x^{2} - \frac{1}{108} (6 e^{6 x} x - e^{6 x}) + C

\int \frac{1}{1} d x

\int \frac{1 - z}{z ^{2} + 2 z + 1} d z

\int \frac{3 x}{( x + 5 ) ^{2}} d x

\int (- 3 x + 5) cos (2 x) d x

\int \frac{1}{6 x ^{2} - 5 x - 6} d x

What is the integral of e^{6x}x^2 ?
The integral of e^{6x}x^2 is 1/6 e^{6x}x^2-1/108 (6e^{6x}x-e^{6x})+C