IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

adithya.bdvt

tan

x dx

bvsatyaram

Dear Aditya,

First take, y =

x, then x=y^2, so, dx=2y dy
Hence, given integral =

(2*y*tan(y))dy
Now for product rule,

UdV = UV-

VdU, take, U=y and dV=tan y
use

tan x = ln |cos x|

Now, u will end up with an expression, where the only term which is unknown is

ln |cos y|dy

ln |cos y|dy=

ln |cos y|*sin y * cosec y * dy

Now take, U=cosec y, and dV = ln |cos y|*sin y
Now u will end up with an expression, where the only unknown is

^{sec y dy
Now}

sec y dy = ln |sec y + tan y|
thats alll!!!