What is the integral of (8-((5^x))/2) ?

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

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integral of (8-((5^x))/2)

\int (8 - \frac{( 5 ^{x} )}{2}) d x

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

Solution steps

\int 8 - \frac{5 ^{x}}{2} 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 8 d x - \int \frac{5 ^{x}}{2} d x

\int 8 d x = 8 x

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

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

Add a constant to the solution

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

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