Exercise
$\int\left(\left(x-1\right)^3\cdot lnx\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int((x-1)^3ln(x))dx. We can solve the integral \int\left(x-1\right)^3\ln\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.
Solve the integral of logarithmic functions int((x-1)^3ln(x))dx
Final answer to the exercise
$\frac{\left(x-1\right)^{4}\ln\left|x\right|}{4}-\frac{1}{4}\ln\left|x\right|+x-\frac{3}{4}x^2+\frac{x^{3}}{3}+\frac{-x^{4}}{16}+C_0$