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Popular Calculus >

integral of 6^{2x}

Solution

\int 6^{2 x} d x

Solution

\frac{9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 6 )} + C

Solution steps

\int 6^{2 x} d x

Simplify

6^{2 x} : 3 6^{x}

= \int 3 6^{x} d x

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

= \frac{3 6 ^{x}}{ln ( 36 )}

Simplify

\frac{3 6 ^{x}}{ln ( 36 )} : \frac{9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 6 )}

= \frac{9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 6 )}

Add a constant to the solution

= \frac{9 ^{x} \cdot 2 ^{2 x - 1}}{ln ( 6 )} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 6^{2x} ?
The integral of 6^{2x} is (9^x*2^{2x-1})/(ln(6))+C