How to find integration of tan3x.tan2x.tanx.? Is t

Question

How to find integration of tan3x.tan2x.tanx.? Is there any easy way to solve it

Vikas TU · Accepted Answer

use standard identities first and then reduc this to an easy expression eqn. then integearte it.

Use, tan(A+B) = (tanA + tanB)/(1 – tanAtanB)

tanAtanB = 1 – (tanA + tanB)/tan(A+B)

for tan2x and tanx,

tan2x.tanx = 1 – (tanx + tan2x)/tan3x = > (tan3x – tanx – tan2x)/tan3x

TThus the expression reduces to:

tan3x*(tan3x – tanx – tan2x)/tan3x

or

dI = (tan3x – tanx – tan2x) dxNow u can integerate easily.

How to find integration of tan3x.tan2x.tanx.? Is there any easy way to solve it