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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(e^{2x})

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

x^{2} + C

Solution steps

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

Apply Integration By Parts

: 2 x^{2} - \int 2 x d x

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

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

= 2 x^{2} - x^{2}

Simplify

= x^{2}

Add a constant to the solution

= x^{2} + C

\int \frac{1 + sin ( 2 x )}{cos ^{2} ( x )} d x

\int \frac{1}{x ( x + 1 ) ( x + 3 )} d x

\int 3 (sin (x))^{- 2} d x

\int 7 x^{5} e^{x^{6}} d x

\int \frac{x ^{3}}{( x ^{4} + 16 ) ^{2}} d x