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

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

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

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

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

Solution steps

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

Expand

\frac{x ^{3} + 1}{x ^{2}} : x + \frac{1}{x ^{2}}

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

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

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

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

Add a constant to the solution

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

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