What is the integral of (3x-1)sqrt(x+6) ?

The integral of (3x-1)sqrt(x+6) is 2x(x+6)^{3/2}-2/3 (x+6)^{3/2}-4/5 (x+6)^{5/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (3x-1)sqrt(x+6)

\int (3 x - 1) x + 6 d x

2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}} + C

Solution steps

\int (3 x - 1) x + 6 d x

Apply Integration By Parts

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \int 2 (x + 6)^{\frac{3}{2}} d x

\int 2 (x + 6)^{\frac{3}{2}} d x = \frac{4}{5} (x + 6)^{\frac{5}{2}}

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}}

Add a constant to the solution

= 2 x (x + 6)^{\frac{3}{2}} - \frac{2}{3} (x + 6)^{\frac{3}{2}} - \frac{4}{5} (x + 6)^{\frac{5}{2}} + C

What is the integral of (3x-1)sqrt(x+6) ?
The integral of (3x-1)sqrt(x+6) is 2x(x+6)^{3/2}-2/3 (x+6)^{3/2}-4/5 (x+6)^{5/2}+C