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. Integrate the function ln(((4x+3)(x+2)^6)/((1-9x)^3)). Find the integral. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Expand the integral \int\left(\ln\left(\left(4x+3\right)\left(x+2\right)^6\right)-\ln\left(\left(1-9x\right)^3\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(\left(4x+3\right)\left(x+2\right)^6\right)dx results in: \frac{1}{4}\left(4x+3+5\right)\left(6\ln\left(4x+3+5\right)+\ln\left(4x+3\right)\right)-\frac{7}{4}\left(4x+3+5\right)-\frac{5}{4}\ln\left(4x+3+5-5\right)-\ln\left(8\right)\left(4x+3\right).