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

The integral of 1/(x+1^5) is ln|x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 1/(x+1^5)

\int \frac{1}{x + 1 ^{5}} d x

ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{1}{x + 1 ^{5}} d x

Simplify

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + 1

= ln ∣ x + 1 ∣

Add a constant to the solution

= ln ∣ x + 1 ∣ + C

\int (3 z^{2} + 1) arctan (z)

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

\int 3 t e^{- s t} d t

\int - sin (x) + e^{x} d x

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