What is the integral of (x^4-5e^{-2x}) ?

The integral of (x^4-5e^{-2x}) is (x^5)/5+5/2 e^{-2x}+C

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integral of (x^4-5e^{-2x})

\int (x^{4} - 5 e^{- 2 x}) d x

\frac{x ^{5}}{5} + \frac{5}{2} e^{- 2 x} + C

Solution steps

\int x^{4} - 5 e^{- 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^{4} d x - \int 5 e^{- 2 x} d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

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

Simplify

= \frac{x ^{5}}{5} + \frac{5}{2} e^{- 2 x}

Add a constant to the solution

= \frac{x ^{5}}{5} + \frac{5}{2} e^{- 2 x} + C

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What is the integral of (x^4-5e^{-2x}) ?
The integral of (x^4-5e^{-2x}) is (x^5)/5+5/2 e^{-2x}+C