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

The integral of e^x(e^x+1) is ((e^x+1)^2)/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^x(e^x+1)

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

\frac{( e ^{x} + 1 ) ^{2}}{2} + C

Solution steps

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

Apply u-substitution

= \int u d u

Apply the Power Rule

= \frac{u ^{2}}{2}

Substitute back

u = e^{x} + 1

= \frac{( e ^{x} + 1 ) ^{2}}{2}

Add a constant to the solution

= \frac{( e ^{x} + 1 ) ^{2}}{2} + C

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