Calculus Examples

Find the Integral (dx)/((2+cos(x)-2sin(x))sin(x))
Step 1
Since is constant with respect to , move out of the integral.
Step 2
By the Power Rule, the integral of with respect to is .
Step 3
Simplify the answer.
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Step 3.1
Rewrite as .
Step 3.2
Simplify.
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Step 3.2.1
Combine and .
Step 3.2.2
Combine and .
Step 3.2.3
Multiply by .
Step 3.2.4
Move to the left of .
Step 3.3
Simplify.
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Step 3.3.1
Simplify the numerator.
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Step 3.3.1.1
Rewrite in terms of sines and cosines.
Step 3.3.1.2
Combine exponents.
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Step 3.3.1.2.1
Combine and .
Step 3.3.1.2.2
Combine and .
Step 3.3.2
Multiply the numerator by the reciprocal of the denominator.
Step 3.3.3
Combine.
Step 3.3.4
Multiply by .
Step 3.3.5
Move to the left of .