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Int. Of 1/1+cotx Full solution

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Int. Of 1/1+cotx Full solution

Posted by Vikrant Dagur 7 years, 10 months ago

CBSE > Class 12 > Mathematics

2 answers

Prabhjot Guraya 7 years, 10 months ago

As given velow

Utsab Mukherjee 7 years, 10 months ago

Home » Forum » Integral Calculus » how to integrate (1)/1+cotx using... how to integrate (1)/1+cotx using substitution metod ? one year ago Answers : (1) 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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