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