What is the integral of 7x^2+8x^{-2} ?

The integral of 7x^2+8x^{-2} is (7x^3)/3-8/x+C

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integral of 7x^2+8x^{-2}

\int 7 x^{2} + 8 x^{- 2} d x

\frac{7 x ^{3}}{3} - \frac{8}{x} + C

Solution steps

\int 7 x^{2} + 8 x^{- 2} d x

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

= \int 7 x^{2} + \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 7 x^{2} d x + \int \frac{8}{x ^{2}} d x

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

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

= \frac{7 x ^{3}}{3} - \frac{8}{x}

Add a constant to the solution

= \frac{7 x ^{3}}{3} - \frac{8}{x} + C

What is the integral of 7x^2+8x^{-2} ?
The integral of 7x^2+8x^{-2} is (7x^3)/3-8/x+C