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

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

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

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

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

Solution steps

\int e^{- \frac{x}{5}} + 5 x^{4} 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^{- \frac{x}{5}} d x + \int 5 x^{4} d x

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

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

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

Add a constant to the solution

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

h (t) = (t + 4)^{\frac{2}{3}} (2 t^{2} - 4)^{3}

x \to 7 lim (sec (\frac{π x}{6}))

\frac{d y}{d x} = 7 x + y

x - x^{3}

\int \frac{1}{x ^{2} - 64} d x

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