What is the integral of 3x^{-3}+4x^2-x^{3/5} ?

The integral of 3x^{-3}+4x^2-x^{3/5} is -3/(2x^2)+(4x^3)/3-5/8 x^{8/5}+C

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integral of 3x^{-3}+4x^2-x^{3/5}

\int 3 x^{- 3} + 4 x^{2} - x^{\frac{3}{5}} d x

- \frac{3}{2 x ^{2}} + \frac{4 x ^{3}}{3} - \frac{5}{8} x^{\frac{8}{5}} + C

Solution steps

\int 3 x^{- 3} + 4 x^{2} - x^{\frac{3}{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 3 x^{- 3} d x + \int 4 x^{2} d x - \int x^{\frac{3}{5}} d x

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

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int x^{\frac{3}{5}} d x = \frac{5}{8} x^{\frac{8}{5}}

= - \frac{3}{2 x ^{2}} + \frac{4 x ^{3}}{3} - \frac{5}{8} x^{\frac{8}{5}}

Add a constant to the solution

= - \frac{3}{2 x ^{2}} + \frac{4 x ^{3}}{3} - \frac{5}{8} x^{\frac{8}{5}} + C

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What is the integral of 3x^{-3}+4x^2-x^{3/5} ?
The integral of 3x^{-3}+4x^2-x^{3/5} is -3/(2x^2)+(4x^3)/3-5/8 x^{8/5}+C