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If int(sinx+3cosx)/(sinx+cosx)dx=(kx)/(2...

If `int(sinx+3cosx)/(sinx+cosx)dx=(kx)/(2)+ln(sinx+cosx)`, then `k` is_________.

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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(cosx)/(sinx+cosx)dx=

    A
    `-log(1+tanx)+c`
    B
    `log(cosx-sinx)+c`
    C
    `log(1-cotx)+c`
    D
    `-log(1+cotx)+c`

  • int(4sinx-38cosx)/(5sinx-11cosx)dx=

    A
    `3x+log|5sinx-11cosx|+c`
    B
    `3x-log|5sinx-11cosx|+c`
    C
    `x+log|5sinx-11cosx|+c`
    D
    `x-log|5sinx-11cosx|+c`