Learn how to solve problems step by step online. Find the integral int((x^(1/2)+1)/(x^(7/6)+3x))dx. Expand the fraction \frac{\sqrt{x}+1}{\sqrt[6]{x^{7}}+3x} into 2 simpler fractions with common denominator \sqrt[6]{x^{7}}+3x. Expand the integral \int\left(\frac{\sqrt{x}}{\sqrt[6]{x^{7}}+3x}+\frac{1}{\sqrt[6]{x^{7}}+3x}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{\sqrt[6]{x^{7}}+3x}dx results in: \frac{1}{3}\ln\left(\sqrt[6]{x^{7}}+3x\right). Gather the results of all integrals.

Find the integral int((x^(1/2)+1)/(x^(7/6)+3x))dx