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

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

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integral of (x^2+2^{-x})

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

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

Solution steps

\int x^{2} + 2^{- 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 x^{2} d x + \int 2^{- x} d x

\int x^{2} d x = \frac{x ^{3}}{3}

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

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

Add a constant to the solution

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

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