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Popular >

integral of 5^{3x}

Solution

\int 5^{3 x} d x

Solution

\frac{12 5 ^{x}}{3 ln ( 5 )} + C

Solution steps

\int 5^{3 x} d x

Simplify

5^{3 x} : 12 5^{x}

= \int 12 5^{x} d x

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

= \frac{12 5 ^{x}}{ln ( 125 )}

Simplify

ln (125) : 3 ln (5)

= \frac{12 5 ^{x}}{3 ln ( 5 )}

Add a constant to the solution

= \frac{12 5 ^{x}}{3 ln ( 5 )} + C

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Frequently Asked Questions (FAQ)

What is the integral of 5^{3x} ?
The integral of 5^{3x} is (125^x)/(3ln(5))+C