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

The integral of 2/4 x^3+x^{-2}+2x is (x^4)/8-1/x+x^2+C

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

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

\frac{x ^{4}}{8} - \frac{1}{x} + x^{2} + C

Solution steps

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

\int \frac{2}{4} x^{3} d x = \frac{x ^{4}}{8}

\int x^{- 2} d x = - \frac{1}{x}

\int 2 x d x = x^{2}

= \frac{x ^{4}}{8} - \frac{1}{x} + x^{2}

Add a constant to the solution

= \frac{x ^{4}}{8} - \frac{1}{x} + x^{2} + C

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What is the integral of 2/4 x^3+x^{-2}+2x ?
The integral of 2/4 x^3+x^{-2}+2x is (x^4)/8-1/x+x^2+C