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Popular Calculus >

integral of 5^{5x}

Solution

\int 5^{5 x} d x

Solution

\frac{5 ^{5 x - 1}}{ln ( 5 )} + C

Solution steps

\int 5^{5 x} d x

Simplify

5^{5 x} : 312 5^{x}

= \int 312 5^{x} d x

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

= \frac{312 5 ^{x}}{ln ( 3125 )}

Simplify

\frac{312 5 ^{x}}{ln ( 3125 )} : \frac{5 ^{5 x - 1}}{ln ( 5 )}

= \frac{5 ^{5 x - 1}}{ln ( 5 )}

Add a constant to the solution

= \frac{5 ^{5 x - 1}}{ln ( 5 )} + C

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the integral of 5^{5x} ?
The integral of 5^{5x} is (5^{5x-1})/(ln(5))+C