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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. Find the integral of (-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. The integral \int-\cos\left(2x\right)dx results in: -\frac{1}{2}\sin\left(2x\right).