What is the integral of (-x^5+6e^{-2x}) ?

The integral of (-x^5+6e^{-2x}) is -(x^6)/6-3e^{-2x}+C

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integral of (-x^5+6e^{-2x})

\int (- x^{5} + 6 e^{- 2 x}) d x

- \frac{x ^{6}}{6} - 3 e^{- 2 x} + C

Solution steps

\int - x^{5} + 6 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^{5} d x + \int 6 e^{- 2 x} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 6 e^{- 2 x} d x = - 3 e^{- 2 x}

= - \frac{x ^{6}}{6} - 3 e^{- 2 x}

Add a constant to the solution

= - \frac{x ^{6}}{6} - 3 e^{- 2 x} + C

(x + y) y^{^{'}} = x - y

\int \frac{1}{x} + 1 d x

\int 3 r^{2} d r

f (x) = x^{2} + 5, at x = 2

y = x^{3} - 4 x, (2, 0)

What is the integral of (-x^5+6e^{-2x}) ?
The integral of (-x^5+6e^{-2x}) is -(x^6)/6-3e^{-2x}+C