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

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

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integral of (5x-5^x)

\int (5 x - 5^{x}) d x

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

Solution steps

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

\int 5 x d x = \frac{5 x ^{2}}{2}

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

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

Add a constant to the solution

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

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