Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- 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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Find the integral
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$\int\left(1+\sin\left(x\right)\right)\left(1+\sin\left(-x\right)\right)dx$
Learn how to solve problems step by step online. Integrate the function (1+sin(x))(1+sin(-x)). Find the integral. Rewrite the integrand \left(1+\sin\left(x\right)\right)\left(1+\sin\left(-x\right)\right) in expanded form. Expand the integral \int\left(1+\sin\left(-x\right)+\sin\left(x\right)+\sin\left(-x\right)\sin\left(x\right)\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\sin\left(x\right)dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula.