Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Weierstrass Substitution
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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$\int\left(-\sin\left(x\right)+\cos\left(x\right)+2\right)\left(-\cos\left(x\right)-\sin\left(x\right)\right)dx$
Learn how to solve problems step by step online. Integrate the function (-sin(x)+cos(x)+2)(-cos(x)-sin(x)). Find the integral. Rewrite the integrand \left(-\sin\left(x\right)+\cos\left(x\right)+2\right)\left(-\cos\left(x\right)-\sin\left(x\right)\right) in expanded form. Expand the integral \int\left(-\cos\left(2x\right)-2\cos\left(x\right)-2\sin\left(x\right)\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int-2\cos\left(x\right)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.