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

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

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integral of 3/(x^5)-2/(x^2)-6/x

\int \frac{3}{x ^{5}} - \frac{2}{x ^{2}} - \frac{6}{x} d x

- \frac{3}{4 x ^{4}} + \frac{2}{x} - 6 ln ∣ x ∣ + C

Solution steps

\int \frac{3}{x ^{5}} - \frac{2}{x ^{2}} - \frac{6}{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 \frac{3}{x ^{5}} d x - \int \frac{2}{x ^{2}} d x - \int \frac{6}{x} d x

\int \frac{3}{x ^{5}} d x = - \frac{3}{4 x ^{4}}

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

= - \frac{3}{4 x ^{4}} - (- \frac{2}{x}) - 6 ln ∣ x ∣

Simplify

= - \frac{3}{4 x ^{4}} + \frac{2}{x} - 6 ln ∣ x ∣

Add a constant to the solution

= - \frac{3}{4 x ^{4}} + \frac{2}{x} - 6 ln ∣ x ∣ + C

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

\int \frac{x + 4}{x ^{2} + 8 x - 20} d x

y^{^{'}} = 2 x y - x

x \to 0 lim (10 - x^{2})

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

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