Final answer to the problem
$\ln\left(\tan\left(\frac{x}{2}\right)+1\right)+\ln\left(\sqrt{\left(\tan\left(\frac{x}{2}\right)+1\right)^2-2}\right)+\frac{-x}{2}-\frac{1}{2}\ln\left(\sec\left(\frac{x}{2}\right)^2\right)+C_1$
Got another answer? Verify it here!
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...
Can't find a method? Tell us so we can add it.
1
Simplify the fraction $\frac{\tan\left(x\right)+1}{\tan\left(x\right)^2-1}$
Learn how to solve problems step by step online.
$\int\frac{1}{\tan\left(x\right)-1}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int((tan(x)+1)/(tan(x)^2-1))dx. Simplify the fraction \frac{\tan\left(x\right)+1}{\tan\left(x\right)^2-1}. We can solve the integral \int\frac{1}{\tan\left(x\right)-1}dx by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get.
Final answer to the problem
$\ln\left(\tan\left(\frac{x}{2}\right)+1\right)+\ln\left(\sqrt{\left(\tan\left(\frac{x}{2}\right)+1\right)^2-2}\right)+\frac{-x}{2}-\frac{1}{2}\ln\left(\sec\left(\frac{x}{2}\right)^2\right)+C_1$
