abhishek singh
Last Activity: 10 Years ago
see , you have to use by parts..
.. for simplification put “ nx “ = “t” … then dx = dt/n , and eax = e(a/n)*t
now , Take COSt as the first part and e(a/n)*t as the second part ..
I =∫-aaeaxcosnxdx
i.e
I =( cost ) * ( e(a/n)*t )*( n/a ) + ∫( sint ) * ( e(a/n)*t )* ( n/a )dt ------------> {1}
= again taking ( sint) as the first part and the other one as second part we can write the later term including integration sign as
( sint ) * ( e(a/n)*t )* ( n/a )* ( n/a ) – ∫(cost) * ( e(a/n)*t )* ( n/a )* ( n/a ) dt
= ( sint ) * ( e(a/n)*t )* ( n/a )* ( n/a ) – I* ( n/a )* ( n/a )
now put this value in equation number {1} . and then solve urselve to get the answer
(a2 /n)*(1/ (a2 + n2 ) )*[eax ] * ( acosnx + nsinnx )