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

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

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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

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