What is the integral of 4^{5x-3} ?

The integral of 4^{5x-3} is (2^{10x-7})/(5ln(2))+C

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integral of 4^{5x-3}

\int 4^{5 x - 3} d x

\frac{2 ^{10 x - 7}}{5 ln ( 2 )} + C

Solution steps

\int 4^{5 x - 3} d x

Simplify

4^{5 x - 3} : 4^{5 x} \cdot 4^{- 3}

= \int 4^{5 x} \cdot 4^{- 3} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4^{- 3} \cdot \int 4^{5 x} d x

4^{- 3} = \frac{1}{64}

= \frac{1}{64} \cdot \int 4^{5 x} d x

Simplify

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

= \frac{1}{64} \cdot \int 102 4^{x} d x

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

= \frac{1}{64} \cdot \frac{102 4 ^{x}}{ln ( 1024 )}

Simplify

\frac{1}{64} \cdot \frac{102 4 ^{x}}{ln ( 1024 )} : \frac{2 ^{10 x - 7}}{5 ln ( 2 )}

= \frac{2 ^{10 x - 7}}{5 ln ( 2 )}

Add a constant to the solution

= \frac{2 ^{10 x - 7}}{5 ln ( 2 )} + C

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What is the integral of 4^{5x-3} ?
The integral of 4^{5x-3} is (2^{10x-7})/(5ln(2))+C