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Integral of sin2x sec^2x dx

Guest May 7, 2017
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Take the integral:
 integral sin(2 x) sec^2(x) dx


Simplify the integrand sin(2 x) sec^2(x) to get 2 tan(x):
 = integral2 tan(x) dx


Factor out constants:
 = 2 integral tan(x) dx


Rewrite tan(x) as (sin(x))/(cos(x)):
 = 2 integral(sin(x))/(cos(x)) dx
For the integrand (sin(x))/(cos(x)), substitute u = cos(x) and du = -sin(x) dx:
 = 2 integral-1/u du


Factor out constants:
 = -2 integral1/u du


The integral of 1/u is log(u):
 = -2 log(u) + constant


Substitute back for u = cos(x):
Answer: | = -2 log(cos(x)) + constant

Guest May 7, 2017

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