What is the integral of 5^{3x+2}+4^{5-x} ?

The integral of 5^{3x+2}+4^{5-x} is (5^{3x+2})/(3ln(5))-(2^{-2x+9})/(ln(2))+C

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integral of 5^{3x+2}+4^{5-x}

\int 5^{3 x + 2} + 4^{5 - x} d x

\frac{5 ^{3 x + 2}}{3 ln ( 5 )} - \frac{2 ^{- 2 x + 9}}{ln ( 2 )} + C

Solution steps

\int 5^{3 x + 2} + 4^{5 - 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^{3 x + 2} d x + \int 4^{5 - x} d x

\int 5^{3 x + 2} d x = \frac{5 ^{3 x + 2}}{3 ln ( 5 )}

\int 4^{5 - x} d x = - \frac{2 ^{- 2 x + 9}}{ln ( 2 )}

= \frac{5 ^{3 x + 2}}{3 ln ( 5 )} - \frac{2 ^{- 2 x + 9}}{ln ( 2 )}

Add a constant to the solution

= \frac{5 ^{3 x + 2}}{3 ln ( 5 )} - \frac{2 ^{- 2 x + 9}}{ln ( 2 )} + C

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What is the integral of 5^{3x+2}+4^{5-x} ?
The integral of 5^{3x+2}+4^{5-x} is (5^{3x+2})/(3ln(5))-(2^{-2x+9})/(ln(2))+C