What is the integral of e^x*2^{e^x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^x*2^{e^x}

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

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

Solution steps

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

Apply u-substitution

: \int 2^{u} d u

= \int 2^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{2 ^{u}}{ln ( 2 )}

Substitute back

u = e^{x}

= \frac{2 ^{e^{x}}}{ln ( 2 )}

Add a constant to the solution

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

\int \frac{- 2 x ^{3} + x + 1}{x ^{4} + 2 x ^{2} + 1} d x

\int sin (a x) \cdot e^{b x} d x

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

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

\int \frac{x ^{2} + 2 x + 1}{x ^{3} - 16 x} d x

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