What is the integral of 8x^7-7/(x^7) ?

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

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integral of 8x^7-7/(x^7)

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

x^{8} + \frac{7}{6 x ^{6}} + C

Solution steps

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

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

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

= x^{8} - (- \frac{7}{6 x ^{6}})

Simplify

= x^{8} + \frac{7}{6 x ^{6}}

Add a constant to the solution

= x^{8} + \frac{7}{6 x ^{6}} + C

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