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

The integral of (6x^5+1/5 x^{-6}) is x^6-1/(25x^5)+C

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integral of (6x^5+1/5 x^{-6})

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

x^{6} - \frac{1}{25 x ^{5}} + C

Solution steps

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

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

\int \frac{1}{5} x^{- 6} d x = - \frac{1}{25 x ^{5}}

= x^{6} - \frac{1}{25 x ^{5}}

Add a constant to the solution

= x^{6} - \frac{1}{25 x ^{5}} + C

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What is the integral of (6x^5+1/5 x^{-6}) ?
The integral of (6x^5+1/5 x^{-6}) is x^6-1/(25x^5)+C