Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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Rewrite the expression $\frac{1}{4x^2-9}$ inside the integral in factored form
Rewrite the fraction $\frac{1}{\left(2x+3\right)\left(2x-3\right)}$ in $2$ simpler fractions using partial fraction decomposition
Expand the integral $\int\left(\frac{-1}{6\left(2x+3\right)}+\frac{1}{6\left(2x-3\right)}\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
The integral $\int\frac{-1}{6\left(2x+3\right)}dx$ results in: $-\frac{1}{12}\ln\left(2x+3\right)$
The integral $\int\frac{1}{6\left(2x-3\right)}dx$ results in: $\frac{1}{12}\ln\left(2x-3\right)$
Gather the results of all integrals
As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration $C$
