Question

Find : \( \int \frac{dx}{x^{1/2} + x^{1/3}} \)

Hint:

Adding and subtracting 1 inside the numerator polynomial (\( t^3 \to t^3+1-1 \)) allows you to use the sum of cubes factorization formula \( a^3+b^3 = (a+b)(a^2-ab+b^2) \), avoiding long polynomial division entirely.

Answer 1