What is the integral of (2x-1)sqrt(x+3) ?

The integral of (2x-1)sqrt(x+3) is 4/5 (x+3)^{5/2}-14/3 (x+3)^{3/2}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-1)sqrt(x+3)

\int (2 x - 1) x + 3 d x

\frac{4}{5} (x + 3)^{\frac{5}{2}} - \frac{14}{3} (x + 3)^{\frac{3}{2}} + C

Solution steps

\int (2 x - 1) x + 3 d x

Expand

(2 x - 1) x + 3 : 2 x x + 3 - x + 3

= \int 2 x x + 3 - x + 3 d x

Apply the Sum Rule:

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

= \int 2 x x + 3 d x - \int x + 3 d x

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

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

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

Simplify

2 (\frac{2}{5} (x + 3)^{\frac{5}{2}} - 2 (x + 3)^{\frac{3}{2}}) - \frac{2}{3} (x + 3)^{\frac{3}{2}} : \frac{4}{5} (x + 3)^{\frac{5}{2}} - \frac{14}{3} (x + 3)^{\frac{3}{2}}

= \frac{4}{5} (x + 3)^{\frac{5}{2}} - \frac{14}{3} (x + 3)^{\frac{3}{2}}

Add a constant to the solution

= \frac{4}{5} (x + 3)^{\frac{5}{2}} - \frac{14}{3} (x + 3)^{\frac{3}{2}} + C

\int ([(3 x)]^{2} + 2 x) (x^{3} + x^{2}) d x

\int 4 \cdot cos^{2} (x) d x

\int (8 y - \frac{2}{y ^{\frac{1}{4}}}) d y

\int \frac{1}{x ^{3}} csc (\frac{1}{x ^{2}}) cot (\frac{1}{x ^{2}}) d x

\int cos^{3} (x) sin^{9} (x) d x

What is the integral of (2x-1)sqrt(x+3) ?
The integral of (2x-1)sqrt(x+3) is 4/5 (x+3)^{5/2}-14/3 (x+3)^{3/2}+C