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
- Load more...
Simplify $\frac{\sin\left(x\right)^5}{\cos\left(x\right)^5}$ into $\tan\left(x\right)^5$ by applying trigonometric identities
Learn how to solve trigonometric integrals problems step by step online.
$\int\tan\left(x\right)^5dx$
Learn how to solve trigonometric integrals problems step by step online. Solve the trigonometric integral int((sin(x)^5)/(cos(x)^5))dx. Simplify \frac{\sin\left(x\right)^5}{\cos\left(x\right)^5} into \tan\left(x\right)^5 by applying trigonometric identities. 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).