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Popular Calculus >

integral of 4^{5x}

Solution

\int 4^{5 x} d x

Solution

\frac{2 ^{10 x - 1}}{5 ln ( 2 )} + C

Solution steps

\int 4^{5 x} d x

Simplify

4^{5 x} : 102 4^{x}

= \int 102 4^{x} d x

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

= \frac{102 4 ^{x}}{ln ( 1024 )}

Simplify

\frac{102 4 ^{x}}{ln ( 1024 )} : \frac{2 ^{10 x - 1}}{5 ln ( 2 )}

= \frac{2 ^{10 x - 1}}{5 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{10 x - 1}}{5 ln ( 2 )} + C

Graph

Popular Examples

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integral of ((x+1)^2)/((x^2+1)^2)

integral of (e^{2x}-1)/(e^x-1)

integral of 1/(sqrt(-x^2-4x+5))

Frequently Asked Questions (FAQ)

What is the integral of 4^{5x} ?
The integral of 4^{5x} is (2^{10x-1})/(5ln(2))+C