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

The integral of ln(x+sqrt(x^2-1)) is xln(x+sqrt(x^2-1))-sqrt(x^2-1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(x+sqrt(x^2-1))

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

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

Solution steps

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

Apply Integration By Parts

: x ln (x + x^{2} - 1) - \int \frac{x}{x ^{2} - 1} d x

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

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

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

Add a constant to the solution

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

y^{^{'}} = - 100 y + 101 cos (t) + 99 sin (t), y (0) = 1

\int (\frac{1}{x} - \frac{2}{9 x ^{2} + 1}) d x

\frac{d}{d x} ((5 x + 1)^{3})

(9.1) (6.5)

\int \frac{3}{y} - \frac{1}{y + 3} d y

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