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Grade: 12
        integrate tanx*tan2x*tan3x dx
8 years ago

Answers : (2)

Sameer Kumar Srivastava
31 Points
							

using tan3x=(tanx+tan2x)/1+tanxtan2x

we have the given integration as ∫(tanx+tan2x-tan3x)

which is equal to ln|secx|+1/2ln|sec2x|-1/3ln|sce3x|

tell me are you satisfied with my solution.

8 years ago
vikas askiitian expert
509 Points
							

I = tanxtan2xtan3xdx              ..............1

 

tan3x = tan(x+2x) = tanx + tan2x/1-tanxtan2x

 

tan3x(1-tanxtan2x) = tanx + tan2x

 

tanxtan2xtan3x =  tan3x - tanx - tan2x  .................2

from 1 & 2

I =( tan3x -tanx -tan2x )dx

I = logsec3x/3 - logsec2x/2 - logsecx + C

  =log[ (sec3x)1/3/(sec2x)1/2(secx) ]  + C

approve if u like it

8 years ago
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