What is the integral of 5/((x+2)^2) ?

The integral of 5/((x+2)^2) is -5/(x+2)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/((x+2)^2)

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

- \frac{5}{x + 2} + C

Solution steps

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

Take the constant out:

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

= 5 \cdot \int \frac{1}{( x + 2 ) ^{2}} d x

Apply u-substitution

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

= 5 \cdot \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= 5 (- \frac{1}{u})

Substitute back

u = x + 2

= 5 (- \frac{1}{x + 2})

Simplify

5 (- \frac{1}{x + 2}) : - \frac{5}{x + 2}

= - \frac{5}{x + 2}

Add a constant to the solution

= - \frac{5}{x + 2} + C

\int \frac{1}{x ^{2} - 81} d x

f (x) = sin (2 x) cos (3 x)

\int 3 sin (5 x + 4) d x

\int_{1}^{16} e^{x} d x

y^{^{''}} + 4 y^{^{'}} + 13 y = 3 cos (2 x)