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

The integral of 1/(sqrt(x+1)+2) is 2(sqrt(x+1)+2-2ln|sqrt(x+1)+2|)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/(sqrt(x+1)+2)

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

2 (x + 1 + 2 - 2 ln x + 1 + 2) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u + 2} d u

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

Apply u-substitution

: \int \frac{2 ( v - 2 )}{v} d v

= \int \frac{2 ( v - 2 )}{v} d v

Take the constant out:

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

= 2 \cdot \int \frac{v - 2}{v} d v

Expand

\frac{v - 2}{v} : 1 - \frac{2}{v}

= 2 \cdot \int 1 - \frac{2}{v} d v

Apply the Sum Rule:

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

= 2 (\int 1 d v - \int \frac{2}{v} d v)

\int 1 d v = v

\int \frac{2}{v} d v = 2 ln ∣ v ∣

= 2 (v - 2 ln ∣ v ∣)

Substitute back

= 2 (x + 1 + 2 - 2 ln x + 1 + 2)

Add a constant to the solution

= 2 (x + 1 + 2 - 2 ln x + 1 + 2) + C

\int x (x + 5)^{5} d x

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

\int sin (5 - 4 x) d x

\int t^{2} e^{8 t} d t

\int cos^{9} (5 t) sin (5 t) d t

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