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

The integral of (3x-1)/(sqrt(x+1)) is 2(x+1)^{3/2}-8sqrt(x+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int \frac{3 x - 1}{x + 1} d x

2 (x + 1)^{\frac{3}{2}} - 8 x + 1 + C

Solution steps

\int \frac{3 x - 1}{x + 1} d x

Expand

\frac{3 x - 1}{x + 1} : \frac{3 x}{x + 1} - \frac{1}{x + 1}

= \int \frac{3 x}{x + 1} - \frac{1}{x + 1} 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 \frac{3 x}{x + 1} d x - \int \frac{1}{x + 1} d x

\int \frac{3 x}{x + 1} d x = 6 (\frac{1}{3} (x + 1)^{\frac{3}{2}} - x + 1)

\int \frac{1}{x + 1} d x = 2 x + 1

= 6 (\frac{1}{3} (x + 1)^{\frac{3}{2}} - x + 1) - 2 x + 1

Simplify

6 (\frac{1}{3} (x + 1)^{\frac{3}{2}} - x + 1) - 2 x + 1 : 2 (x + 1)^{\frac{3}{2}} - 8 x + 1

= 2 (x + 1)^{\frac{3}{2}} - 8 x + 1

Add a constant to the solution

= 2 (x + 1)^{\frac{3}{2}} - 8 x + 1 + C

\frac{\partial}{\partial x} (y - x^{2} - x y^{2})

\int_{1}^{3} 3 x^{2} + \frac{1}{12 x ^{2}} d x

x \to 3 lim (- 4)

13 e^{4 t} \cdot e^{2}

\int_{\frac{1}{2}}^{5} 10 x ln (2 x) d x

What is the integral of (3x-1)/(sqrt(x+1)) ?
The integral of (3x-1)/(sqrt(x+1)) is 2(x+1)^{3/2}-8sqrt(x+1)+C