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Evaluate: int{1+2tanx(tanx+secx))^(1/2)...

Evaluate: `int{1+2tanx(tanx+secx))^(1/2)dx`

Text Solution

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`I=int{1+2tanx(tanx+secx)}^(1/2)dx`
`I=int{(1+2tan^2x+2tanxsecx)^(1/2)dx`
`I=int{(1+tan^2x+tan^2x+2tanxsecx)^(1/2)dx`
`I=int{(sec^2x+tan^2x+2tanxsecx)^(1/2)dx`
`I=int{(secx+tanx)^(2/2)dx`
`I=int{(secx+tanx)dx`
`I=int(secx)dx+int (tanx)dx`
`I=log|secx+tanx|+log|secx|+c`
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