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Exercise

$\int\left(cosx\right)\left(1-sinx\right)^3dx$

Step-by-step Solution

1

Simplify $\cos\left(x\right)\left(1-\sin\left(x\right)\right)^3$ into $\cos\left(x\right)-3\sin\left(x\right)\cos\left(x\right)+3\sin\left(x\right)^2\cos\left(x\right)-\sin\left(x\right)^3\cos\left(x\right)$ by applying trigonometric identities

$\int\left(\cos\left(x\right)-3\sin\left(x\right)\cos\left(x\right)+3\sin\left(x\right)^2\cos\left(x\right)-\sin\left(x\right)^3\cos\left(x\right)\right)dx$

Final answer to the exercise

$\int\left(\cos\left(x\right)-3\sin\left(x\right)\cos\left(x\right)+3\sin\left(x\right)^2\cos\left(x\right)-\sin\left(x\right)^3\cos\left(x\right)\right)dx$

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