What is the integral of e^{ln(x^2+1)} ?

The integral of e^{ln(x^2+1)} is (x^3)/3+x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{ln(x^2+1)}

\int e^{l n (x^{2} + 1)} d x

\frac{x ^{3}}{3} + x + C

Solution steps

\int e^{l n (x^{2} + 1)} d x

Apply log rule:

a^{l o g_{a} (b)} = b

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int x^{2} d x = \frac{x ^{3}}{3}

\int 1 d x = x

= \frac{x ^{3}}{3} + x

Add a constant to the solution

= \frac{x ^{3}}{3} + x + C

\int \frac{1}{y} e^{- (y + \frac{x}{y})} d x

\int - \frac{1}{x ln ( x )} d x

\int e^{x} (sin (x))^{2} d x

\int x^{4} 1 + x^{5} d x

\int cos^{4} (3 t) sin (3 t) d t

What is the integral of e^{ln(x^2+1)} ?
The integral of e^{ln(x^2+1)} is (x^3)/3+x+C