What is the integral of (x^4)/2-x+2/(x^3) ?

The integral of (x^4)/2-x+2/(x^3) is (x^5}{10}-\frac{x^2)/2-1/(x^2)+C

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integral of (x^4)/2-x+2/(x^3)

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

\frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

Solution steps

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

\int \frac{x ^{4}}{2} d x = \frac{x ^{5}}{10}

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

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

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}}

Add a constant to the solution

= \frac{x ^{5}}{10} - \frac{x ^{2}}{2} - \frac{1}{x ^{2}} + C

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What is the integral of (x^4)/2-x+2/(x^3) ?
The integral of (x^4)/2-x+2/(x^3) is (x^5}{10}-\frac{x^2)/2-1/(x^2)+C