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if tanx=4/3Then Find (2sinx-3cosx)/(2sin...

if `tanx=4/3`Then Find `(2sinx-3cosx)/(2sinx+3cosx)`

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intcosx/(2sinx+3cosx)dx

int(2sinx+3cosx)/(3sinx+4cosx)dx =?

Knowledge Check

  • int(sinx+cosx)/(3sinx+4cosx)dx=

    A
    `(1)/(25)(11x+2log|3sinx+4cosx|)+c`
    B
    `(1)/(25)(11x-2log|3sinx+4cosx|)+c`
    C
    `(1)/(25)(11x+log|3sinx+4cosx|)+c`
    D
    `(1)/(25)(11x-log|3sinx+4cosx|)+c`

  • int(3sinx+5cosx+4)/(sinx+cosx+2)dx=

    A
    `log(sinx+cosx+2)+4x-4tan^(-1)(1+tan""(x)/(2))+c`
    B
    `log(sinx+cosx+2)+4x-4sqrt2tan^(-1)((1+tan""(x)/(2))/(sqrt2))+c`
    C
    `4log(sinx+cosx+2)+x-4sqrt2tan^(-1)((1+tan""(x)/(2))/(sqrt2))+c`
    D
    `4log(sinx+cosx+2)+4x-4sqrt2tan^(-1)((1-tan""(x)/(2))/(sqrt2))+c`

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