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

\frac{x + 1}{x + 5}

\frac{d}{d x} (x e^{x} + x - 5 e^{x} - 5)

y = x sin (\frac{2}{x})

\int 4 t + 1 d t

\frac{x + 9}{x ^{2} - 7 x + 1}

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