What is the integral of (e^{-12x}+11^x) ?

The integral of (e^{-12x}+11^x) is -1/12 e^{-12x}+(11^x)/(ln(11))+C

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integral of (e^{-12x}+11^x)

\int (e^{- 12 x} + 1 1^{x}) d x

- \frac{1}{12} e^{- 12 x} + \frac{1 1 ^{x}}{ln ( 11 )} + C

Solution steps

\int e^{- 12 x} + 1 1^{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 e^{- 12 x} d x + \int 1 1^{x} d x

\int e^{- 12 x} d x = - \frac{1}{12} e^{- 12 x}

\int 1 1^{x} d x = \frac{1 1 ^{x}}{ln ( 11 )}

= - \frac{1}{12} e^{- 12 x} + \frac{1 1 ^{x}}{ln ( 11 )}

Add a constant to the solution

= - \frac{1}{12} e^{- 12 x} + \frac{1 1 ^{x}}{ln ( 11 )} + C

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What is the integral of (e^{-12x}+11^x) ?
The integral of (e^{-12x}+11^x) is -1/12 e^{-12x}+(11^x)/(ln(11))+C