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Popular >

integral of 5^{10x}

Solution

\int 5^{10 x} d x

Solution

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

Solution steps

\int 5^{10 x} d x

Simplify

5^{10 x} : 976562 5^{x}

= \int 976562 5^{x} d x

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

= \frac{976562 5 ^{x}}{ln ( 9765625 )}

Simplify

\frac{976562 5 ^{x}}{ln ( 9765625 )} : \frac{5 ^{10 x - 1}}{2 ln ( 5 )}

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

Add a constant to the solution

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

Popular Examples

integral of sqrt(10+\sqrt{x)}

\int 10 + x d x

integral of (e^xsin(x))/(sec(x))

\int \frac{e ^{x} sin ( x )}{sec ( x )} d x

integral of (5x^2+10x-30)/(x^2+x-6)

\int \frac{5 x ^{2} + 10 x - 30}{x ^{2} + x - 6} d x

integral of (e^x)/(e^{2x)+2e^x-8}

\int \frac{e ^{x}}{e ^{2 x} + 2 e ^{x} - 8} d x

integral of ((9-4x^2)^{3/2})/(x^6)

\int \frac{( 9 - 4 x ^{2} ) ^{\frac{3}{2}}}{x ^{6}} d x

Frequently Asked Questions (FAQ)

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