Exercise
$\int\ln\left|x\right|^26x^3-6x^3\int\left(6x^3\right)\frac{2}{x}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the integral of logarithmic functions int(ln(x)^26x^3-6x^3int(6x^32/x)dx)dx. Simplify the expression. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as 2. Simplify the expression. The integral \int6\ln\left(x\right)^2x^3dx results in: \frac{3}{2}x^{4}\ln\left(x\right)^2-\frac{3}{4}x^{4}\ln\left(x\right)+\frac{3x^{4}}{16}.
Solve the integral of logarithmic functions int(ln(x)^26x^3-6x^3int(6x^32/x)dx)dx
Final answer to the exercise
$\frac{3x^{4}}{16}-\frac{3}{4}x^{4}\ln\left|x\right|+\frac{3}{2}x^{4}\ln\left|x\right|^2-\frac{24}{7}x^{7}+C_0$