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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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