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integrate the following integral ∫ cos x cos 2x cos 3x dx

 
integrate the following integral
∫ cos x cos 2x cos 3x dx

Grade:12

1 Answers

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

I = \int cosx.cos2x.cos3xdx
I = \int (cosx.cos3x).cos2xdx
I = \frac{1}{2}\int (cos2x+cos4x).cos2xdx
I = \frac{1}{2}\int (cos^{2}2x+cos4xcos2x)dx
I = \frac{1}{2}\int cos^{2}2xdx+\frac{1}{2}\int cos4xcos2xdx
I = \frac{1}{4}\int (1+cos4x)dx+\frac{1}{4}\int (cos2x+cos6x)dx
I = \frac{1}{4}(x+\frac{sin4x}{4})+\frac{1}{4}\int (cos2x+cos6x)dx
I = \frac{1}{4}(x+\frac{sin4x}{4})+\frac{1}{4}(\frac{sin2x}{2}+\frac{sin6x}{6})+c
I = \frac{1}{4}(x+\frac{sin4x}{4}+\frac{sin2x}{2}+\frac{sin6x}{6})+c

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