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

The integral of 2^x*2^{2x} is (8^x)/(3ln(2))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{8 ^{x}}{3 ln ( 2 )} + C

Solution steps

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

Simplify

2^{x} \cdot 2^{2 x} : 8^{x}

= \int 8^{x} d x

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

= \frac{8 ^{x}}{ln ( 8 )}

Simplify

ln (8) : 3 ln (2)

= \frac{8 ^{x}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{8 ^{x}}{3 ln ( 2 )} + C

\int 12 - 3 t^{2} d t

\int 5 t^{3} d t

\int \frac{5 x ^{2} - 5}{x ^{3} - 9 x ^{2} + 23 x - 15} d x

\int sin^{8} (\frac{3}{4}) x \cdot cos^{6} (\frac{3}{4}) x d x

\int \frac{x ^{3} + x ^{2} + x - 5}{x ^{2} + 2 x + 4} d x

What is the integral of 2^x*2^{2x} ?
The integral of 2^x*2^{2x} is (8^x)/(3ln(2))+C