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Evaluate: int(2sinx+3cosx)/(3sinx+4cosx)...

Evaluate: `int(2sinx+3cosx)/(3sinx+4cosx)\ dx`

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To evaluate the integral \[ I = \int \frac{2 \sin x + 3 \cos x}{3 \sin x + 4 \cos x} \, dx, \] we can use the method of integration by parts or substitution. Here, we will use the method of substitution. ...
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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(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`
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