IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

puneetagr1

plz solv integral of "xtanx"

vinod

Here is the answer !! Although I could not slove it

vasanth

let me try

integration by parts

u.dv = uv -

v.du

dv = tanx

so v = log secx

u = x

du = 1

so using integration by parts

x.tanx = x logsecx -

log secx

even if we take

dv = x; u = tanx

we will get stuck in a step similar to this....

i believe that it is a polylogrithmic fn.......neone plz help!

cheers!

ALTERNATE TRY:

tanx = (e^2ix - 1)/(e^2i(x+pi/4)+ i)

try this.....i'm not sure whether this will yield the result......

vinod's method makes use of "i"

so this tan function has to be either hyperbolic or expressed by using complex nos.....in the given Q it is not hyperbolic.......

i donno whether we can use

itanhx = tan ix

i cant proceed from here........plz help guys.....

^{do rate ma effort ppl!}

cheers!

vinod

Yes vasanth same case with me toooooooo... i tooo am stuck !

no still i am stuck

prvn_iit07

Integrate[x Tan[x], x] ==
I 2 (2 I) x
- x - x Log[1 + E ] +
2
I (2 I) x
- PolyLog[2, -E ]
2

OR

Integrate[x*Tan[x], x] ==

(I/2)*x^2 - x*Log[1 + E^((2*I)*x)] + (I/2)*PolyLog[2, -E^((2*I)*x)]

Log[x]: : natural logarithm [properties]
PolyLog[n, x]: : polylogarithm function [properties]

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