What is the integral of 1/(x^7)-x^7-1/2 ?

The integral of 1/(x^7)-x^7-1/2 is -1/(6x^6)-(x^8)/8-1/2 x+C

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integral of 1/(x^7)-x^7-1/2

\int \frac{1}{x ^{7}} - x^{7} - \frac{1}{2} d x

- \frac{1}{6 x ^{6}} - \frac{x ^{8}}{8} - \frac{1}{2} x + C

Solution steps

\int \frac{1}{x ^{7}} - x^{7} - \frac{1}{2} 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 ^{7}} d x - \int x^{7} d x - \int \frac{1}{2} d x

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}}

\int x^{7} d x = \frac{x ^{8}}{8}

\int \frac{1}{2} d x = \frac{1}{2} x

= - \frac{1}{6 x ^{6}} - \frac{x ^{8}}{8} - \frac{1}{2} x

Add a constant to the solution

= - \frac{1}{6 x ^{6}} - \frac{x ^{8}}{8} - \frac{1}{2} x + C

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What is the integral of 1/(x^7)-x^7-1/2 ?
The integral of 1/(x^7)-x^7-1/2 is -1/(6x^6)-(x^8)/8-1/2 x+C