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integrate the following integral ∫ (1 + cos 4x)/cot x – tan x dx

 
integrate the following integral
∫ (1 + cos 4x)/cot x – tan x dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{1+cos4x}{cotx-tanx}dx
I = \int \frac{2cos^{2}2x}{\frac{cosx}{sinx}-\frac{sinx}{cosx}}dx
I = \int \frac{2cos^{2}2x.(sinxcosx)}{cos^{2}x-sin^{2}x}dx
I = \int \frac{2cos^{2}2x.(sinxcosx)}{cos2x}dx
I = \int \frac{cos^{2}2x.sin2x}{cos2x}dx
I = \int (cos2x.sin2x)dx
I = \int \frac{sin4x}{2}dx
I = \frac{-cos4x}{8}+c

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