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Find the value of ∫(sinx/sin4x)dx= ∫sinx/2sin2x cos2x)dx ∫sinx/4sinx cosx cos2x)dx

Find the value of ∫(sinx/sin4x)dx=
∫sinx/2sin2x cos2x)dx
∫sinx/4sinx cosx cos2x)dx

Grade:12

1 Answers

Aditya Gupta
2075 Points
2 years ago
∫sinx/4sinx cosx cos2x)dx= ∫1/4cosx cos2x)dx
put sinx=y, it becomes
∫dy/(1 – y^2)(1 – 2y^2)
now use partial fractions to obtain the integral in terms of log function and then finally replace y with sinx.
note that the method which i have given is the shortest and easiest method. but i cannot write the entire answer f the integral as it is TOOO LONG to be contained here.
 

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