Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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$\int\ln\left(\frac{\left(4x+3\right)\left(x+2\right)^6}{\left(1-9x\right)^3}\right)dx$
Learn how to solve 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. We can solve the integral \int\ln\left(\left(4x+3\right)\left(x+2\right)^6\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 4x+3 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.