+0  
 
0
234
1
avatar

Integral of sin2x sec^2x dx

Guest May 7, 2017
 #1
avatar
0

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

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.