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Solution to a trigonometric problem requested by one student

B.Sudhakar
14/01/2017 0 0

∫ sin² x /( 1+ cos x ) dx 

Let's multiply both numerator and denominator by ( 1 - cos x )

= ∫ sin² x • ( 1 - cos x ) / ( 1 + cos x ) • ( 1 - cos x ) dx 

= ∫ sin² x • (1 - cos x ) / ( 1 - cos² x ) dx 

= ∫ sin² x • ( 1 - cos x ) / ( sin² x ) dx         ( 1 - cos² x = sin² x )

= ∫ ( 1 - cos x ) dx         ( sin² x   cancels out )

= ∫ 1• dx - ∫ cos x dx 

= x - sin x + C

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