What is the integral of (-5x^{-3}+5x^5) ?

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

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integral of (-5x^{-3}+5x^5)

\int (- 5 x^{- 3} + 5 x^{5}) d x

\frac{5}{2 x ^{2}} + \frac{5 x ^{6}}{6} + C

Solution steps

\int - 5 x^{- 3} + 5 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 5 x^{- 3} d x + \int 5 x^{5} d x

\int 5 x^{- 3} d x = - \frac{5}{2 x ^{2}}

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

= - (- \frac{5}{2 x ^{2}}) + \frac{5 x ^{6}}{6}

Simplify

= \frac{5}{2 x ^{2}} + \frac{5 x ^{6}}{6}

Add a constant to the solution

= \frac{5}{2 x ^{2}} + \frac{5 x ^{6}}{6} + C

x \to \infty lim (\frac{1}{x} + 4)

\int sin (x) 2 x d x

x \to \frac{π}{2} + lim (e^{t a n (x)})

q \to 0 lim (9 q + 3)

\int e^{9 x} cos (7 x) d x

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