What is the integral of (1/5-2/(x^3)+2x) ?

The integral of (1/5-2/(x^3)+2x) is 1/5 x+1/(x^2)+x^2+C

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integral of (1/5-2/(x^3)+2x)

\int (\frac{1}{5} - \frac{2}{x ^{3}} + 2 x) d x

\frac{1}{5} x + \frac{1}{x ^{2}} + x^{2} + C

Solution steps

\int \frac{1}{5} - \frac{2}{x ^{3}} + 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{1}{5} d x - \int \frac{2}{x ^{3}} d x + \int 2 x d x

\int \frac{1}{5} d x = \frac{1}{5} x

\int \frac{2}{x ^{3}} d x = - \frac{1}{x ^{2}}

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

= \frac{1}{5} x - (- \frac{1}{x ^{2}}) + x^{2}

Simplify

= \frac{1}{5} x + \frac{1}{x ^{2}} + x^{2}

Add a constant to the solution

= \frac{1}{5} x + \frac{1}{x ^{2}} + x^{2} + C

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What is the integral of (1/5-2/(x^3)+2x) ?
The integral of (1/5-2/(x^3)+2x) is 1/5 x+1/(x^2)+x^2+C