Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- Integrate by partial fractions
- 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
- FOIL Method
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Rewrite the trigonometric expression $\frac{1}{\cos\left(x\right)+\sin\left(x\right)+1}$ inside the integral
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$\int\frac{\cos\left(x\right)+\sin\left(x\right)-1}{\left(\cos\left(x\right)+\sin\left(x\right)\right)^2-1\cdot 1^2}dx$
Learn how to solve problems step by step online. Solve the trigonometric integral int(1/(cos(x)+sin(x)+1))dx. Rewrite the trigonometric expression \frac{1}{\cos\left(x\right)+\sin\left(x\right)+1} inside the integral. Calculate the power 1^2. Expand the expression \left(\cos\left(x\right)+\sin\left(x\right)\right)^2 using the square of a binomial: (a+b)^2=a^2+2ab+b^2. Simplify the expression inside the integral.