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Popular Calculus >

integral of 6^{3x}

Solution

\int 6^{3 x} d x

Solution

\frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )} + C

Solution steps

\int 6^{3 x} d x

Simplify

6^{3 x} : 21 6^{x}

= \int 21 6^{x} d x

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

= \frac{21 6 ^{x}}{ln ( 216 )}

Simplify

\frac{21 6 ^{x}}{ln ( 216 )} : \frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )}

= \frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )}

Add a constant to the solution

= \frac{8 ^{x} \cdot 3 ^{3 x - 1}}{ln ( 6 )} + C

Graph

Popular Examples

integral of x^{(1/3)}

\int x^{(\frac{1}{3})} d x

integral of 4cosh(x)+x^2

\int 4 cosh (x) + x^{2} d x

integral of 1/(6u)

\int \frac{1}{6 u} d u

integral of 5/(x-7)

\int \frac{5}{x - 7} d x

integral of (30)/(sqrt(2t+4))

\int \frac{30}{2 t + 4} d t

Frequently Asked Questions (FAQ)

What is the integral of 6^{3x} ?
The integral of 6^{3x} is (8^x*3^{3x-1})/(ln(6))+C