Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate using trigonometric identities
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
Applying a reduction formula for the integral of the tangent function: $\displaystyle\int\tan(x)^{n}dx=\frac{1}{n-1}\tan(x)^{n-1}-\int\tan(x)^{n-2}dx$
Simplify the expression inside the integral
The integral $-\int\tan\left(x\right)^{3}dx$ results in: $-\frac{1}{2}\sec\left(x\right)^2-\ln\left(\cos\left(x\right)\right)$
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 $C$