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

The integral of (6x^{3/2}+5x^{-2}) is 12/5 x^{5/2}-5/x+C

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

\int (6 x^{\frac{3}{2}} + 5 x^{- 2}) d x

\frac{12}{5} x^{\frac{5}{2}} - \frac{5}{x} + C

Solution steps

\int 6 x^{\frac{3}{2}} + 5 x^{- 2} d x

5 x^{- 2} = \frac{5}{x ^{2}}

= \int 6 x^{\frac{3}{2}} + \frac{5}{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 6 x^{\frac{3}{2}} d x + \int \frac{5}{x ^{2}} d x

\int 6 x^{\frac{3}{2}} d x = \frac{12}{5} x^{\frac{5}{2}}

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

= \frac{12}{5} x^{\frac{5}{2}} - \frac{5}{x}

Add a constant to the solution

= \frac{12}{5} x^{\frac{5}{2}} - \frac{5}{x} + C

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What is the integral of (6x^{3/2}+5x^{-2}) ?
The integral of (6x^{3/2}+5x^{-2}) is 12/5 x^{5/2}-5/x+C