Exercise
$\int\left(x-a\right)^3\ln\left(x-a\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int((x-a)^3ln(x-a))dx. We can solve the integral \int\left(x-a\right)^3\ln\left(x-a\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.
Solve the integral of logarithmic functions int((x-a)^3ln(x-a))dx
Final answer to the exercise
$\frac{\left(x-a\right)^{4}\ln\left|x-a\right|}{4}+\frac{-\left(x-a\right)^{4}}{16}+C_0$