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Popular >

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

Popular Examples

integral of x/(sqrt(5-4x))

\int \frac{x}{5 - 4 x} d x

integral of (cos(2x))/(cos(x)+sin(x))

\int \frac{cos ( 2 x )}{cos ( x ) + sin ( x )} d x

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

\int \frac{1}{x} + \frac{1}{x ^{2} + 1} d x

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

\int \frac{( x + 1 ) ^{2}}{( x ^{2} + 1 ) ^{2}} d x

integral of 2/(sqrt(-x^2-2x))

\int \frac{2}{- x ^{2} - 2 x} d x

Frequently Asked Questions (FAQ)

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