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})

\int (11 x + 12 x) d x

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

Solution steps

\int 11 x + 12 x 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 d x + \int 12 x d x

\int 11 x d x = \frac{11}{12} x^{\frac{12}{11}}

\int 12 x d x = \frac{12}{13} x^{\frac{13}{12}}

= \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

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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