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Evaluate int tan x tan(x+1)dx....

Evaluate `int tan x tan(x+1)dx`.

Text Solution

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`tan 1 =(tan(x+1)-tanx)/(1+tanx tan(x+1))`
` :. tanx tan(x+1)=tan(x+1)-tan x=tan 1`
` :. int tanx tan(x+1)dx`
`=int(tan(x+1)-tanx-tan 1)dx`
`=log_(e)|sec(x+1)|-log_(e)|sec x|-(tan 1)x +c`
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