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

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

Grade:12th pass

1 Answers

Vikas TU
14149 Points
5 years ago
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.
 
 
 
 

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