What is the integral of (4x-36)/(sqrt(x)+3) ?

The integral of (4x-36)/(sqrt(x)+3) is -12x+8/3 x^{3/2}-216+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (4x-36)/(sqrt(x)+3)

\int \frac{4 x - 36}{x + 3} d x

- 12 x + \frac{8}{3} x^{\frac{3}{2}} - 216 + C

Solution steps

\int \frac{4 x - 36}{x + 3} d x

Expand

\frac{4 x - 36}{x + 3} : \frac{4 x}{x + 3} - \frac{36}{x + 3}

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{4 x}{x + 3} d x - \int \frac{36}{x + 3} d x

\int \frac{4 x}{x + 3} d x = 8 (\frac{1}{3} x^{\frac{3}{2}} - \frac{3 x}{2} + 9 x - 27 ln x + 3)

\int \frac{36}{x + 3} d x = 72 (x + 3 - 3 ln x + 3)

= 8 (\frac{1}{3} x^{\frac{3}{2}} - \frac{3 x}{2} + 9 x - 27 ln x + 3) - 72 (x + 3 - 3 ln x + 3)

Simplify

8 (\frac{1}{3} x^{\frac{3}{2}} - \frac{3 x}{2} + 9 x - 27 ln x + 3) - 72 (x + 3 - 3 ln x + 3) : - 12 x + \frac{8}{3} x^{\frac{3}{2}} - 216

= - 12 x + \frac{8}{3} x^{\frac{3}{2}} - 216

Add a constant to the solution

= - 12 x + \frac{8}{3} x^{\frac{3}{2}} - 216 + C

\int (5 x^{- 4} - 3) d x

\int \frac{9}{9 + x ^{2}} d x

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

\int \frac{x - 2}{( 2 x ^{2} + 2 x + 1 ) ^{2}} d x

\int \frac{4 ( t ^{2} + 3 )}{t ( t ^{2} + 6 )} d t

What is the integral of (4x-36)/(sqrt(x)+3) ?
The integral of (4x-36)/(sqrt(x)+3) is -12x+8/3 x^{3/2}-216+C