Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate using tabular integration
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- 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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Applying a reduction formula for the integral of the tangent function: $\displaystyle\int\tan(x)^{n}dx=\frac{1}{n-1}\tan(x)^{n-1}-\int\tan(x)^{n-2}dx$
Learn how to solve trigonometric integrals problems step by step online.
$\frac{1}{5-1}\tan\left(x\right)^{4}-\int\tan\left(x\right)^{3}dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int(tan(x)^5)dx. 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.