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

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

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integral of (5x^2+6x^{-2})

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

\frac{5 x ^{3}}{3} - \frac{6}{x} + C

Solution steps

\int 5 x^{2} + 6 x^{- 2} d x

6 x^{- 2} = \frac{6}{x ^{2}}

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

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

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

= \frac{5 x ^{3}}{3} - \frac{6}{x}

Add a constant to the solution

= \frac{5 x ^{3}}{3} - \frac{6}{x} + C

\int \frac{1}{x ln ^{p} ( x )} d x

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\int \frac{x + 3}{( x ^{2} + 2 x + 3 ) ^{2}} d x

\int c e^{- a x} d x

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