What is the integral of ((x^6-5x)/(x^2)) ?

The integral of ((x^6-5x)/(x^2)) is (x^5)/5-5ln|x|+C

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integral of ((x^6-5x)/(x^2))

\int (\frac{x ^{6} - 5 x}{x ^{2}}) d x

\frac{x ^{5}}{5} - 5 ln ∣ x ∣ + C

Solution steps

\int \frac{x ^{6} - 5 x}{x ^{2}} d x

Simplify

\frac{x ^{6} - 5 x}{x ^{2}} : \frac{x ^{5} - 5}{x}

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

Expand

\frac{x ^{5} - 5}{x} : x^{4} - \frac{5}{x}

= \int x^{4} - \frac{5}{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 x^{4} d x - \int \frac{5}{x} d x

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{5}}{5} - 5 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{5}}{5} - 5 ln ∣ x ∣ + C

x \to 0 lim (\frac{x}{sin ( \frac{x}{2} )})

\frac{d}{d x} (\frac{- 3 x ^{4} - 5 x ^{3} + 2}{- 5 x ^{4}})

\frac{\partial}{\partial x} (\frac{1}{1 + x})

\frac{\partial}{\partial x} (x^{2} - 2 x^{2} y - 5 x y^{2})

\int (2 x)^{2} (5 + 3^{4})^{\frac{1}{4}} d x

What is the integral of ((x^6-5x)/(x^2)) ?
The integral of ((x^6-5x)/(x^2)) is (x^5)/5-5ln|x|+C