What is the integral of 5-(8/(x^2)) ?

The integral of 5-(8/(x^2)) is 5x+8/x+C

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integral of 5-(8/(x^2))

integral

5 - (\frac{8}{x ^{2}})

5 x + \frac{8}{x} + C

Solution steps

\int 5 - \frac{8}{x ^{2}} 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 d x - \int \frac{8}{x ^{2}} d x

\int 5 d x = 5 x

\int \frac{8}{x ^{2}} d x = - \frac{8}{x}

= 5 x - (- \frac{8}{x})

Simplify

= 5 x + \frac{8}{x}

Add a constant to the solution

= 5 x + \frac{8}{x} + C

2 x^{3} (e^{x})^{- 2}

x^{3} (a^{3} - x^{3})^{5}

x (1 + x)^{3}

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

\frac{x + 1}{( x )}