What is the integral of (x^6-5x)/(x^4) ?

The integral of (x^6-5x)/(x^4) is (x^3)/3+5/(2x^2)+C

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integral of (x^6-5x)/(x^4)

\int \frac{x ^{6} - 5 x}{x ^{4}} d x

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

Solution steps

\int \frac{x ^{6} - 5 x}{x ^{4}} d x

Expand

\frac{x ^{6} - 5 x}{x ^{4}} : x^{2} - \frac{5}{x ^{3}}

= \int x^{2} - \frac{5}{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 x^{2} d x - \int \frac{5}{x ^{3}} d x

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

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}}

= \frac{x ^{3}}{3} - (- \frac{5}{2 x ^{2}})

Simplify

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

Add a constant to the solution

= \frac{x ^{3}}{3} + \frac{5}{2 x ^{2}} + C

\frac{d}{d x} (e^{2} (sin (\frac{π}{4}) - 1))

\frac{s - 1}{2 s ^{2} + 8 s + 11}

1 + 5 x

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

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

What is the integral of (x^6-5x)/(x^4) ?
The integral of (x^6-5x)/(x^4) is (x^3)/3+5/(2x^2)+C