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# Indefinite Integral – A quotient of functions with a root and a third root – Exercise 1982

Exercise

Evaluate the integral

$$\int \frac{1}{\sqrt{x}+\sqrt[3]{x}} dx$$

$$\int \frac{1}{\sqrt{x}+\sqrt[3]{x}} dx =2x^2-3\sqrt[3]{x}+6\sqrt[6]{x}-6\ln|\sqrt[6]{x}+1|+c$$