What is the integral of 11x^{4/7}+6x^{-6/7} ?

The integral of 11x^{4/7}+6x^{-6/7} is 7x^{11/7}+42x^{1/7}+C

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integral of 11x^{4/7}+6x^{-6/7}

\int 11 x^{\frac{4}{7}} + 6 x^{- \frac{6}{7}} d x

7 x^{\frac{11}{7}} + 42 x^{\frac{1}{7}} + C

Solution steps

\int 11 x^{\frac{4}{7}} + 6 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 11 x^{\frac{4}{7}} d x + \int 6 x^{- \frac{6}{7}} d x

\int 11 x^{\frac{4}{7}} d x = 7 x^{\frac{11}{7}}

\int 6 x^{- \frac{6}{7}} d x = 42 x^{\frac{1}{7}}

= 7 x^{\frac{11}{7}} + 42 x^{\frac{1}{7}}

Add a constant to the solution

= 7 x^{\frac{11}{7}} + 42 x^{\frac{1}{7}} + C

\int 5 x - x d x

\frac{1 + x}{2}

- 2 x^{2}, at x = 0

\frac{d}{d x} (\frac{2}{e ^{x} + \frac{1}{e ^{x}}})

What is the integral of 11x^{4/7}+6x^{-6/7} ?
The integral of 11x^{4/7}+6x^{-6/7} is 7x^{11/7}+42x^{1/7}+C