Integration of : (xtanx)dx?

Question

or the integration of log(sinx),

Answer 1

Hi Rony ;

∫x tan(x) dx = (I/2)*x^2 - x*Log[1 + e^((2*I)*x)] + (I/2)*Poly Log[2, -e^((2*I)*x)] + c

∫log(sinx) dx = - (x*Log[1 - e^((2*I)*x)]) + x*Log[Sin[x]] + (I/2)*(x^2 + Poly Log[2, e^((2*I)*x)]) + c

Good Luck Ronny.

Answer 2

Both these integrals are nonelementary.
To integrate x tan x use parts to reduce
the problem to integrating log(cos x).
The integrals of both log(sin x) and log(cos x)
both involve the dilogarithm function.

Answer 3

Integration of : (xtanx)dx =
c ln |cos x| + cx + x sinx + cos x - d

Answer 4

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Answer 5

integration by parts

Answer 6

real solutions of these integrations are not possible. solution will include complex terms.