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int ((1+cosx)/(1-cosx)) dx...

`int ((1+cosx)/(1-cosx)) dx`

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`int ((1+cosx)/(1-cosx)) dx`
`I=int ((1+cosx)/(1-cosx)) dx`
`I=int ((1+cosx)(1+cosx))/((1-cosx)(1+cosx)) dx`
`I=int ((1+cosx)^2)/(1-cos^2x) dx`
`I=int((1+cos^2x+2cosx)/sin^2x)dx`
`I=int(1/sin^2x)dx+intcos^2x/sin^2xdx+int(2cosx)/sin^2xdx`
`I=intcosec^2xdx+intcot^2xdx+2intcosecxcotxdx`
`I=intcosec^2xdx+int(cosec^2x−1)dx+2intcosecxcotxdx`
...
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Knowledge Check

  • int(cosx)/(1-cosx)dx=

    A
    `2cot((x)/(2))+x+c`
    B
    `2cot((x)/(2))-x+c`
    C
    `cot((x)/(2))+x+c`
    D
    `-cot((x)/(2))-x+c`

  • int(sqrt(1+cosx))/(1-cosx)dx=

    A
    `-sqrt2 cosec((x)/(2))+c`
    B
    `sqrt2 cos ((x)/(2))+c`
    C
    `-sqrt2 sec((x)/(2))+c`
    D
    `log[cos((x)/(2))]+c`

  • int (cosx-cos2x)/(1-cosx) dx

    A
    ` 2 sin x + x + C`
    B
    ` 2 sin x - x + C`
    C
    ` cos x + x + C`
    D
    ` 2 cos x + x + C`

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    int(1-cosx)/(cosx(1+cosx))dx

    int_0^pi sqrt(1+cosx)/(1-cosx)^(5//2) dx

    int(dx)/(cosx(1-cosx))=

    int(cosx)/(1+cosx)dx=

    int(cosx)/((1+cosx))dx=?

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