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Popular >

integral of 4^{5t}

Solution

\int 4^{5 t} d t

Solution

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

Solution steps

\int 4^{5 t} d t

Simplify

4^{5 t} : 102 4^{t}

= \int 102 4^{t} d t

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

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

Simplify

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

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

Add a constant to the solution

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

Popular Examples

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\int 2 cos (x) + 2 x d x

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

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\int (x^{2} + 1) cos (3 x) d x

integral of y/(1+3y^2)

\int \frac{y}{1 + 3 y ^{2}} d y

integral of sqrt(1+x^2)x^3

\int 1 + x^{2} x^{3} d x

Frequently Asked Questions (FAQ)

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