What is the integral of (4/(x^5)-5/(x^2)+7/x) ?

The integral of (4/(x^5)-5/(x^2)+7/x) is -1/(x^4)+5/x+7ln|x|+C

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integral of (4/(x^5)-5/(x^2)+7/x)

\int (\frac{4}{x ^{5}} - \frac{5}{x ^{2}} + \frac{7}{x}) d x

- \frac{1}{x ^{4}} + \frac{5}{x} + 7 ln ∣ x ∣ + C

Solution steps

\int \frac{4}{x ^{5}} - \frac{5}{x ^{2}} + \frac{7}{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{4}{x ^{5}} d x - \int \frac{5}{x ^{2}} d x + \int \frac{7}{x} d x

\int \frac{4}{x ^{5}} d x = - \frac{1}{x ^{4}}

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

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= - \frac{1}{x ^{4}} - (- \frac{5}{x}) + 7 ln ∣ x ∣

Simplify

= - \frac{1}{x ^{4}} + \frac{5}{x} + 7 ln ∣ x ∣

Add a constant to the solution

= - \frac{1}{x ^{4}} + \frac{5}{x} + 7 ln ∣ x ∣ + C

What is the integral of (4/(x^5)-5/(x^2)+7/x) ?
The integral of (4/(x^5)-5/(x^2)+7/x) is -1/(x^4)+5/x+7ln|x|+C