Exercise
$\int x^3\cdot\cos^{-1}\left(x\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(x^3arccos(x))dx. We can solve the integral \int x^3\arccos\left(x\right)dx 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.
Find the integral int(x^3arccos(x))dx
Final answer to the exercise
$\frac{x^{4}\arccos\left(x\right)}{4}-\frac{3}{32}x\sqrt{1-x^2}+\frac{3}{32}\arcsin\left(x\right)+\frac{-x^{3}\sqrt{1-x^2}}{16}+C_0$