IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

sabya_sachi

Integrate w.r.t x

1/ ( sinx + xcosx) dx

ruhi

hey some one plz try out this ques. its a gud one..............

KAB

We know sinx=(e^ix-e^-ix)/(2i) and cosx=(e^ix+e^-ix)/2

So given integral is

2idx/((e^ix-e^-ix)+xi(e^ix+e^-ix)

=

2ie^xdx/(e^2ix(1+xi)+(xi-1))

Put e^ix=t

ie^ixdx=dt

So =2

dt/(t²(logt+1)+(logt-1))

Can anyone help me from here.Also tell me whether this is the right approach or not!!!

madhuri_goteti

wat u did is rite kab

ruhi

hey kab i think now we ve 2 apply by parts................but it will b very complicated

madhuri_goteti

kab heres salute for u

KAB

Thanks.May be there is another method.Experts plz help!!!

ruhi

sumone plzzzz try this ques

ruhi

madhuri how do u know that the kab's soln is correct...............ques is nt solved yet................but its a gud try by kab

madhuri_goteti

that is a very good try isn't it??

sabya_sachi

substituting further from kab's soln log t = u

1/t = du/dt this gives integ of 2 e ^u du / e^u *( e^2u -1 ) + u (e^2u + 1 )

now can any one help how to go further

amar.gupta

Dear sabya_sachi

please check and conform whether it is a definite integral or indefinite. if definite please give the limits too.