Find :
 
 
integral fraction numerator x space d x over denominator 1 space plus space x tan x end fraction

Asked by Manisha Behera | 18th Mar, 2015, 03:30: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space i n t e g r a l. I equals integral fraction numerator x d x over denominator 1 plus x tan x end fraction R e w r i t i n g space t h e space a b o v e space e q u a t i o n space a s I equals integral fraction numerator x cos x d x over denominator cos x plus x sin x end fraction S u b s t i t u t e space u equals x sin x plus cos x D i f f e r e n t i a t i n g space t h e space a b o v e comma space w e space h a v e comma rightwards double arrow open parentheses x cos x plus sin x minus sin x close parentheses d x equals d u rightwards double arrow x cos x d x equals d u T h u s comma space I equals integral fraction numerator d u over denominator u end fraction T h e r e f o r e comma space I equals log u plus C rightwards double arrow I equals log open parentheses x sin x plus cos x close parentheses plus C

Answered by Vimala Ramamurthy | 19th Mar, 2015, 09:29: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.