What is the integral of 1/((5-x)^2) ?

The integral of 1/((5-x)^2) is 1/(5-x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((5-x)^2)

\int \frac{1}{( 5 - x ) ^{2}} d x

\frac{1}{5 - x} + C

Solution steps

\int \frac{1}{( 5 - x ) ^{2}} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

: - \frac{1}{u}

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

Substitute back

u = 5 - x

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

Simplify

= \frac{1}{5 - x}

Add a constant to the solution

= \frac{1}{5 - x} + C

\int \frac{e ^{x + 3}}{x} d x

\int (3 x + 2) (x + 3) d x

\int \frac{cos ( x )}{2 + cos ( x )} d x

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