What is the integral of 10x^{3/7}+7x^{-6/7} ?

The integral of 10x^{3/7}+7x^{-6/7} is 7x^{10/7}+49x^{1/7}+C

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integral of 10x^{3/7}+7x^{-6/7}

\int 10 x^{\frac{3}{7}} + 7 x^{- \frac{6}{7}} d x

7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}} + C

Solution steps

\int 10 x^{\frac{3}{7}} + 7 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 10 x^{\frac{3}{7}} d x + \int 7 x^{- \frac{6}{7}} d x

\int 10 x^{\frac{3}{7}} d x = 7 x^{\frac{10}{7}}

\int 7 x^{- \frac{6}{7}} d x = 49 x^{\frac{1}{7}}

= 7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}}

Add a constant to the solution

= 7 x^{\frac{10}{7}} + 49 x^{\frac{1}{7}} + C

x \to 10 lim (x^{2})

y^{^{''}} + 0.2121 y^{^{'}} + 2 y = cos (4 x), y (0) = 0

\int \frac{( ln ( x ^{15} ) )}{x} d x

5 x e^{x}

\frac{2 x ^{3} - 4 x ^{2} + 3}{x}

What is the integral of 10x^{3/7}+7x^{-6/7} ?
The integral of 10x^{3/7}+7x^{-6/7} is 7x^{10/7}+49x^{1/7}+C