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int tan 2x tan3x tan5x dx....

`int tan 2x tan3x tan5x dx.`

Text Solution

Verified by Experts

We know that
`tan5x=tan(3x+2x)`
`tan5x=(tan3x+tan2x​)/(1−tan3x.tan2x)`
`tan5x−tan3xtan2xtan5x=tan3x+tan2x`
`tan5xtan3xtan2x=tan5x−tan3x−tan2x`
`inttan5xtan3xtan2x`
=`inttan5x−inttan3x−inttan2x`
...
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