What is the integral of 2x^3-20x^{-5} ?

The integral of 2x^3-20x^{-5} is (x^4)/2+5/(x^4)+C

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integral of 2x^3-20x^{-5}

\int 2 x^{3} - 20 x^{- 5} d x

\frac{x ^{4}}{2} + \frac{5}{x ^{4}} + C

Solution steps

\int 2 x^{3} - 20 x^{- 5} 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^{3} d x - \int 20 x^{- 5} d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 20 x^{- 5} d x = - \frac{5}{x ^{4}}

= \frac{x ^{4}}{2} - (- \frac{5}{x ^{4}})

Simplify

= \frac{x ^{4}}{2} + \frac{5}{x ^{4}}

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{5}{x ^{4}} + C

n = 0 \sum \infty \frac{2 ^{n}}{8 ^{n}}

\frac{d}{d x} (4 x + \frac{3}{x})

\frac{e ^{- s}}{s ^{2} + 1}

\frac{d}{d x} (8 x - \frac{3}{x})

\frac{d}{d x} (e^{x} x^{2} - e^{x})

What is the integral of 2x^3-20x^{-5} ?
The integral of 2x^3-20x^{-5} is (x^4)/2+5/(x^4)+C