What is the integral of (e^{5x}+1)e^x ?

The integral of (e^{5x}+1)e^x is e^x(e^{5x}+1)-5/6 e^{6x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^{5x}+1)e^x

\int (e^{5 x} + 1) e^{x} d x

e^{x} (e^{5 x} + 1) - \frac{5}{6} e^{6 x} + C

Solution steps

\int (e^{5 x} + 1) e^{x} d x

Apply Integration By Parts

: e^{x} (e^{5 x} + 1) - \int 5 e^{6 x} d x

= e^{x} (e^{5 x} + 1) - \int 5 e^{6 x} d x

\int 5 e^{6 x} d x = \frac{5}{6} e^{6 x}

= e^{x} (e^{5 x} + 1) - \frac{5}{6} e^{6 x}

Add a constant to the solution

= e^{x} (e^{5 x} + 1) - \frac{5}{6} e^{6 x} + C

\int cos (\frac{x}{10}) d x

\int tan^{3} (x) (sec (x)) d x

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

\int - cos (x) (e^{- x}) d x

\int x e^{x} + 2 d x

What is the integral of (e^{5x}+1)e^x ?
The integral of (e^{5x}+1)e^x is e^x(e^{5x}+1)-5/6 e^{6x}+C