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

The integral of 2/(sqrt(x+1)) is 4sqrt(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 2/(sqrt(x+1))

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

4 x + 1 + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int 2 d u

= 2 \cdot \int 2 d u

Integral of a constant:

\int a d x = a x

= 2 \cdot 2 u

Substitute back

u = x + 1

= 2 \cdot 2 x + 1

Simplify

= 4 x + 1

Add a constant to the solution

= 4 x + 1 + C

\int \frac{2 x ^{2} + x}{( 8 x ^{3} + 6 x ^{2} ) ^{2}} d x

\int \frac{2 - x}{4 - x ^{2}} d x

\int \frac{I n x}{x ^{3}} d x

\int \frac{4}{x + 4} d x

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

What is the integral of 2/(sqrt(x+1)) ?
The integral of 2/(sqrt(x+1)) is 4sqrt(x+1)+C