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

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

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

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

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

Solution steps

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

Expand

\frac{x ^{3} + 5}{x ^{2}} : x + \frac{5}{x ^{2}}

= \int x + \frac{5}{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{5}{x ^{2}} d x

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

\int \frac{5}{x ^{2}} d x = - \frac{5}{x}

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

Add a constant to the solution

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

x \to - 2 lim (∣ x + 2 ∣)

\int \frac{7}{x ^{2} x ^{2} - 16} d x

d er i v a t i v e \frac{1}{2} e^{2 x}

\frac{d}{d x} (3 x - 2 y^{4})

\int \frac{5}{x ^{3} - 27} d x

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