What is the integral of 2x^{-1/7}+8 ?

The integral of 2x^{-1/7}+8 is 7/3 x^{6/7}+8x+C

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integral of 2x^{-1/7}+8

\int 2 x^{- \frac{1}{7}} + 8 d x

\frac{7}{3} x^{\frac{6}{7}} + 8 x + C

Solution steps

\int 2 x^{- \frac{1}{7}} + 8 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 2 x^{- \frac{1}{7}} d x + \int 8 d x

\int 2 x^{- \frac{1}{7}} d x = \frac{7}{3} x^{\frac{6}{7}}

\int 8 d x = 8 x

= \frac{7}{3} x^{\frac{6}{7}} + 8 x

Add a constant to the solution

= \frac{7}{3} x^{\frac{6}{7}} + 8 x + C

What is the integral of 2x^{-1/7}+8 ?
The integral of 2x^{-1/7}+8 is 7/3 x^{6/7}+8x+C