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Evaluate: int1/((x-alpha)(beta-x))dx ,(b...

Evaluate: `int1/((x-alpha)(beta-x))dx ,(beta>alpha)`

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We have given
`int1/((x-alpha)(beta-x))dx`
`x=alphacos^2theta+betacos^2theta`
`x−alpha=alphasin^2theta+betacos^2theta−alpha`
`=(beta−alpha)cos^2theta`
`beta−x=beta−alphasin^2theta−betacos^2theta`
`=(beta−alpha)sin^2alpha`
`dx=[alpha.2sinthetacostheta+beta2costheta(−sintheta)]`
...
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Knowledge Check

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    A
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  • int _(alpha)^(beta) sqrt((x-alpha)/(beta -x)) dx is equal to

    A
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    B
    `pi/2 (beta-alpha)`
    C
    ` pi (alpha-beta)`
    D
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  • If alpha, beta be the roots of the quadratic equation 3x^(2)-6x+4=0 , find the value of ((alpha)/(beta)+(beta)/(alpha))+2((1)/(alpha)+(1)/(beta))+3alpha beta :

    A
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    B
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