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int ((sqrt(tanx))/(sinx cosx))dx...

`int ((sqrt(tanx))/(sinx cosx))dx`

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`int(sqrt(tanx))/(sinx cosx)dx=int(sqrt(tanx)(1)/("cos"^(2)x))/((sinx cosx)/("cos"^(2)x))dx`
`=int(sqrt(tanx)sec^(2)x)/(tanx)dx=int(tan x)^(-1//2)sec^(2)x dx`
`=((tan x)^(1//2))/(1//2)+C=2 sqrt(tanx)+C`
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Knowledge Check

  • int(sinx)/(sinx-cosx)dx=

    A
    `(1)/(2).log(sinx-cosx)+c`
    B
    `(1)/(2).[log(sinx-cosx)+x]+c`
    C
    `(1)/(2).log(cosx-sinx)+x+c`
    D
    `(1)/(2).[log(cosx-sinx)+x]+c`

  • int(In(tanx))/(sinx cosx)dx " is equal to "

    A
    `(1)/(2)In(tanx)+c`
    B
    `(1)/(2)In(tan^(2)x)+c`
    C
    `(1)/(2)(In(tanx))^(2)+c`
    D
    non of these

  • int(sinx)/((sinx-cosx))dx=?

    A
    `(1)/(2)x-(1)/(2)log|sinx-cosx|+C`
    B
    `(1)/(2)x+(1)/(2)log|sinx-cosx|+C`
    C
    `log|sinx-cosx|+C`
    D
    none of these

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