Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve integral calculus problems step by step online.
$\int\ln\left(\frac{\left(4x+3\right)\left(x+2\right)^6}{\left(1-9x\right)^3}\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral of ln(((4x+3)(x+2)^6)/((1-9x)^3)). Find the integral. Apply properties of logarithms to expand and simplify the logarithmic expression \ln\left(\frac{\left(4x+3\right)\left(x+2\right)^6}{\left(1-9x\right)^3}\right) inside the integral. Expand the integral \int\left(\ln\left(4x+3\right)+6\ln\left(x+2\right)-3\ln\left(1-9x\right)\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(4x+3\right)dx results in: \frac{1}{4}\left(\left(4x+3\right)\ln\left(4x+3\right)-4x-3\right).