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Popular >

integral of 5^{2x}

Solution

\int 5^{2 x} d x

Solution

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

Solution steps

\int 5^{2 x} d x

Simplify

5^{2 x} : 2 5^{x}

= \int 2 5^{x} d x

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

= \frac{2 5 ^{x}}{ln ( 25 )}

Simplify

ln (25) : 2 ln (5)

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

Add a constant to the solution

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

Popular Examples

derivative of (ln(2x)^2)

\frac{d}{d x} ((ln (2 x))^{2})

integral of (x^2-2x+4)

\int (x^{2} - 2 x + 4) d x

(2x^2-ye^x)dx-e^xdy=0

(2 x^{2} - y e^{x}) d x - e^{x} d y = 0

integral of (ln(t))/t

\int \frac{ln ( t )}{t} d t

derivative of (1+e^x^{-2})

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

Frequently Asked Questions (FAQ)

What is the integral of 5^{2x} ?
The integral of 5^{2x} is (25^x)/(2ln(5))+C