What is the integral of 3/(x^4)-2/x ?

The integral of 3/(x^4)-2/x is -1/(x^3)-2ln|x|+C

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integral of 3/(x^4)-2/x

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

- \frac{1}{x ^{3}} - 2 ln ∣ x ∣ + C

Solution steps

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

\int \frac{3}{x ^{4}} d x = - \frac{1}{x ^{3}}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - \frac{1}{x ^{3}} - 2 ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x ^{3}} - 2 ln ∣ x ∣ + C

What is the integral of 3/(x^4)-2/x ?
The integral of 3/(x^4)-2/x is -1/(x^3)-2ln|x|+C