Integrate the functions`1/(x^(1/2)+x^(1/3))`[Hint: `1/(x^(1/2)+x^(1/3))=1/(x^(1/3)(1+x^(1/6))`, put `x = t^6`]

Explanation

To solve the integral \( \int \frac{1}{\sqrt{x} + x^{1/3}} \, dx \), we can follow these steps:

### Step 1: Rewrite the integrand
We start by factoring out \( x^{1/3} \) from the denominator:
\[ \int \frac{1}{\sqrt{x} + x^{1/3}} \, dx = \int \frac{1}{x^{1/3} \left( x^{1/6} + 1 \right)} \, dx \]

...