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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

ln x^{2} + 2 x - 1 + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{2} + 2 x - 1

= ln x^{2} + 2 x - 1

Add a constant to the solution

= ln x^{2} + 2 x - 1 + C

\int 4 x^{2} sin (π x) d x

\frac{\partial}{\partial x} (ln (2 x^{2} y))

\int \frac{2}{1 + x ^{2}} - \frac{4}{x} d x

y = 25 - x^{2}

x + 1, 0

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