What is the integral of (2^{-x}+9x^2e^{x^3}) ?

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

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integral of (2^{-x}+9x^2e^{x^3})

\int (2^{- x} + 9 x^{2} e^{x^{3}}) d x

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

Solution steps

\int 2^{- x} + 9 x^{2} e^{x^{3}} 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 2^{- x} d x + \int 9 x^{2} e^{x^{3}} d x

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

\int 9 x^{2} e^{x^{3}} d x = 3 e^{x^{3}}

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

Add a constant to the solution

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

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