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Evaluate: int1/(sinx+cosx)\ dx...

Evaluate: `int1/(sinx+cosx)\ dx`

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`int1/(sinx+cosx)\ dx`
`=int frac{sin^2x}{sinxcosx}+frac{cos^2x}{sinx cosx}dx`
`=int tanx+ cotx dx`
`=log secc+(-log cosecx)+C`
`=log abs(tan x)+C`
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Knowledge Check

  • int(1)/(sinx-cosx)dx=

    A
    `(1)/(sqrt2)log[tan((pi)/(4)-(x)/(8))]+c`
    B
    `(1)/(sqrt2)log[cot((pi)/(4)-(x)/(8))]+c`
    C
    `(1)/(sqrt2)tan((x)/(2)-(pi)/(8))+c`
    D
    `(1)/(sqrt2)log[tan((x)/(2)-(pi)/(8))]+c`

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