What is the integral of (1/(x^5)-x^5-1/6) ?

The integral of (1/(x^5)-x^5-1/6) is -1/(4x^4)-(x^6)/6-1/6 x+C

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integral of (1/(x^5)-x^5-1/6)

\int (\frac{1}{x ^{5}} - x^{5} - \frac{1}{6}) d x

- \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{6} x + C

Solution steps

\int \frac{1}{x ^{5}} - x^{5} - \frac{1}{6} 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{1}{x ^{5}} d x - \int x^{5} d x - \int \frac{1}{6} d x

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

\int x^{5} d x = \frac{x ^{6}}{6}

\int \frac{1}{6} d x = \frac{1}{6} x

= - \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{6} x

Add a constant to the solution

= - \frac{1}{4 x ^{4}} - \frac{x ^{6}}{6} - \frac{1}{6} x + C

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What is the integral of (1/(x^5)-x^5-1/6) ?
The integral of (1/(x^5)-x^5-1/6) is -1/(4x^4)-(x^6)/6-1/6 x+C