What is the integral of \sqrt[11]{x}+\sqrt[12]{x} ?

The integral of \sqrt[11]{x}+\sqrt[12]{x} is 11/12 x^{12/11}+12/13 x^{13/12}+C

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integral of \sqrt[11]{x}+\sqrt[12]{x}

\frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}} + C

Solution steps

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}}

Add a constant to the solution

= \frac{11}{12} x^{\frac{12}{11}} + \frac{12}{13} x^{\frac{13}{12}} + C

What is the integral of \sqrt[11]{x}+\sqrt[12]{x} ?
The integral of \sqrt[11]{x}+\sqrt[12]{x} is 11/12 x^{12/11}+12/13 x^{13/12}+C