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

\frac{d}{d x} (8 x - x^{2})

n = 0 \sum \infty cos (n)

x \to 0 lim (e^{s i n (x^{2})})

\int (x - 1)^{2} (sin (x))^{2} d x

f (t) = 1.3 e^{0.7 t}

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