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how to integrate (1)/1+cotx using substitution metod ?

how to integrate (1)/1+cotx using substitution metod ?

Grade:12

1 Answers

DR STRANGE
212 Points
4 years ago
HI Alan,
here isthe solutuion,
     ∫ [ 1 / ( 1 + cos x/sin x ) ] dx 

. = ∫ [ ( sin x ) / ( sin x + cos x ) ] dx 

. = (1/2) • ∫ [ ( 2 sin x ) / ( sin x + cos x ) ] dx ...( Note This Step )

. = (1/2) • ∫ { [ ( sin x + cos x ) - ( cos x - sin x ) ] / ( sin x + cos x ) } dx ... This Too 

. = (1/2) • { ∫ 1 dx - ∫ [ ( cos x - sin x ) / ( sin x + cos x ) ] dx } 

. = (1/2) • { x - ∫ (1/u) du }, ... where ... u = sin x + cos x 

. = ( x/2 ) - (1/2)· ln | u | + C 

. = ( x/2 ) - (1/2)· ln | sin x + cos x | + C .................ans
 plz approve if you are satisfied :)

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