Find the integral $\int\frac{1+\frac{\sqrt{x}}{2}}{1+\frac{\sqrt{x}}{3}}dx$

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$3\int\frac{\sqrt{x}+2}{2\left(\sqrt{x}+3\right)}dx$

Learn how to solve problems step by step online. Find the integral int((1+(x^1/2)/2)/(1+(x^1/2)/3))dx. Simplify the expression inside the integral. Take the constant \frac{1}{2} out of the integral. Multiply 3 times \frac{1}{2}. We can solve the integral \int\frac{\sqrt{x}+2}{\sqrt{x}+3}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sqrt{x} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.