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`        integrate tanx*tan2x*tan3x dx`
6 years ago

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.
```
6 years ago
510 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
```
6 years ago
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