Exercise
$\frac{2}{3}\int\left(\frac{1}{1+\frac{4}{3}x^2}\right)dx$
Step-by-step Solution
Learn how to solve integration by substitution problems step by step online. Find the integral 2/3int(1/(1+4/3x^2))dx. Solve the integral applying the substitution u^2=\frac{4}{3}x^2. Then, take the square root of both sides, simplifying we have. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by finding the derivative of the equation above. Isolate dx in the previous equation. After replacing everything and simplifying, the integral results in.
Find the integral 2/3int(1/(1+4/3x^2))dx
Final answer to the exercise
$\frac{\sqrt{3}\arctan\left(\frac{2}{\sqrt{3}}x\right)}{3}+C_0$