What is the integral of 120x(2x+120)^4 ?

The integral of 120x(2x+120)^4 is 12x(2x+120)^5-(2x+120)^6+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 120x(2x+120)^4

\int 120 x (2 x + 120)^{4} d x

12 x (2 x + 120)^{5} - (2 x + 120)^{6} + C

Solution steps

\int 120 x (2 x + 120)^{4} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 120 \cdot \int x (2 x + 120)^{4} d x

Apply Integration By Parts

= 120 (\frac{1}{10} x (2 x + 120)^{5} - \int \frac{1}{10} (2 x + 120)^{5} d x)

\int \frac{1}{10} (2 x + 120)^{5} d x = \frac{1}{120} (2 x + 120)^{6}

= 120 (\frac{1}{10} x (2 x + 120)^{5} - \frac{1}{120} (2 x + 120)^{6})

Simplify

120 (\frac{1}{10} x (2 x + 120)^{5} - \frac{1}{120} (2 x + 120)^{6}) : 12 x (2 x + 120)^{5} - (2 x + 120)^{6}

= 12 x (2 x + 120)^{5} - (2 x + 120)^{6}

Add a constant to the solution

= 12 x (2 x + 120)^{5} - (2 x + 120)^{6} + C

What is the integral of 120x(2x+120)^4 ?
The integral of 120x(2x+120)^4 is 12x(2x+120)^5-(2x+120)^6+C