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