What is the integral of 5^{2x-1}-2^{3x} ?

The integral of 5^{2x-1}-2^{3x} is (5^{2x-1})/(2ln(5))-(8^x)/(3ln(2))+C

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integral of 5^{2x-1}-2^{3x}

\int 5^{2 x - 1} - 2^{3 x} d x

\frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )} + C

Solution steps

\int 5^{2 x - 1} - 2^{3 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 5^{2 x - 1} d x - \int 2^{3 x} d x

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

\int 2^{3 x} d x = \frac{8 ^{x}}{3 ln ( 2 )}

= \frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )}

Add a constant to the solution

= \frac{5 ^{2 x - 1}}{2 ln ( 5 )} - \frac{8 ^{x}}{3 ln ( 2 )} + C

What is the integral of 5^{2x-1}-2^{3x} ?
The integral of 5^{2x-1}-2^{3x} is (5^{2x-1})/(2ln(5))-(8^x)/(3ln(2))+C