What is the integral of 4/(sqrt(4-(x+2)^2)) ?

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

\int \frac{4}{4 - ( x + 2 ) ^{2}} d x

4 arcsin (\frac{1}{2} x + 1) + C

Solution steps

\int \frac{4}{4 - ( x + 2 ) ^{2}} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{4 - ( x + 2 ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{4 - u ^{2}} d u

= 4 \cdot \int \frac{1}{4 - u ^{2}} d u

Apply Trigonometric Substitution

: \int 1 d v

= 4 \cdot \int 1 d v

Integral of a constant:

\int a d x = a x

= 4 \cdot 1 \cdot v

Substitute back

= 4 \cdot 1 \cdot arcsin (\frac{1}{2} (x + 2))

Simplify

4 \cdot 1 \cdot arcsin (\frac{1}{2} (x + 2)) : 4 arcsin (\frac{1}{2} x + 1)

= 4 arcsin (\frac{1}{2} x + 1)

Add a constant to the solution

= 4 arcsin (\frac{1}{2} x + 1) + C

\int \frac{cos ^{5} ( x )}{sin ^{4} ( x )} d x

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

\int \frac{1}{x 4 x + 25} d x

\int \frac{3}{x ^{2} - 2 x} d x

\int 2 e^{x} + 1 d x

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