Exercise
$\int_0^{\frac{\pi}{3}}xtan^2\left(x\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function xtan(x)^2 from 0 to pi/3. We can solve the integral \int x\tan\left(x\right)^2dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v. Solve the integral to find v.
Integrate the function xtan(x)^2 from 0 to pi/3
Final answer to the exercise
$\frac{- \pi ^2}{9}+\tan\left(\frac{\pi }{3}\right)\cdot \frac{\pi }{3}+\frac{\pi ^2}{18}+\ln\left(\frac{1}{2}\right)$