What is the integral of 12x^{5/7}+5x^{-6/7} ?

The integral of 12x^{5/7}+5x^{-6/7} is 7x^{12/7}+35x^{1/7}+C

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integral of 12x^{5/7}+5x^{-6/7}

\int 12 x^{\frac{5}{7}} + 5 x^{- \frac{6}{7}} d x

7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}} + C

Solution steps

\int 12 x^{\frac{5}{7}} + 5 x^{- \frac{6}{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 12 x^{\frac{5}{7}} d x + \int 5 x^{- \frac{6}{7}} d x

\int 12 x^{\frac{5}{7}} d x = 7 x^{\frac{12}{7}}

\int 5 x^{- \frac{6}{7}} d x = 35 x^{\frac{1}{7}}

= 7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}}

Add a constant to the solution

= 7 x^{\frac{12}{7}} + 35 x^{\frac{1}{7}} + C

What is the integral of 12x^{5/7}+5x^{-6/7} ?
The integral of 12x^{5/7}+5x^{-6/7} is 7x^{12/7}+35x^{1/7}+C