What is the integral of 5^x-e^x+6 ?

The integral of 5^x-e^x+6 is (5^x)/(ln(5))-e^x+6x+C

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integral of 5^x-e^x+6

\int 5^{x} - e^{x} + 6 d x

\frac{5 ^{x}}{ln ( 5 )} - e^{x} + 6 x + C

Solution steps

\int 5^{x} - e^{x} + 6 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 e^{x} d x + \int 6 d x

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

\int e^{x} d x = e^{x}

\int 6 d x = 6 x

= \frac{5 ^{x}}{ln ( 5 )} - e^{x} + 6 x

Add a constant to the solution

= \frac{5 ^{x}}{ln ( 5 )} - e^{x} + 6 x + C

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What is the integral of 5^x-e^x+6 ?
The integral of 5^x-e^x+6 is (5^x)/(ln(5))-e^x+6x+C