What is the integral of (-20x^3-6x^{-3}) ?

The integral of (-20x^3-6x^{-3}) is -5x^4+3/(x^2)+C

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integral of (-20x^3-6x^{-3})

\int (- 20 x^{3} - 6 x^{- 3}) d x

- 5 x^{4} + \frac{3}{x ^{2}} + C

Solution steps

\int - 20 x^{3} - 6 x^{- 3} d x

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

= \int - 20 x^{3} - \frac{6}{x ^{3}} 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 20 x^{3} d x - \int \frac{6}{x ^{3}} d x

\int 20 x^{3} d x = 5 x^{4}

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

= - 5 x^{4} - (- \frac{3}{x ^{2}})

Simplify

= - 5 x^{4} + \frac{3}{x ^{2}}

Add a constant to the solution

= - 5 x^{4} + \frac{3}{x ^{2}} + C

\frac{\partial}{\partial x} (\frac{7 y - 7 x}{y ^{2} + 2 x ^{2}})

(x^{2} - 2 x - 2 sin (x - 2))^{^{'}}

x \to 2 lim (4 ln (2))

n = 1 \sum \infty \frac{n !}{n !}

\int x cos (n x π) d x

What is the integral of (-20x^3-6x^{-3}) ?
The integral of (-20x^3-6x^{-3}) is -5x^4+3/(x^2)+C