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int (3cos x+2 sin x)/(4 cos x+3 sin x)dx...

`int (3cos x+2 sin x)/(4 cos x+3 sin x)dx=`

A

`(1)/(25)log|4cos x+3 sinx|+(18)/(25)x+c`

B

`(1)/(25)log|4cos x+3 sinx|-(18)/(25)x+c`

C

`(1)/(25)log|4cos x-3 sinx|+(18)/(25)x+c`

D

none

Text Solution

Verified by Experts

The correct Answer is:
A
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Knowledge Check

  • int (3 cos 3x-2 sin 2x)/(cos 2x+ sin 3x)dx=

    A
    `-log |cos 2x-sin 3x|+c`
    B
    `log |cos 2x-sin 3x|+c`
    C
    `log |cos 2x+sin 3x|+c`
    D
    none

  • A: int (2cos x +3sin x)/(4cos x+5 sin x)dx= (-2)/(41)log|4cos x+5Sinx|+(23)/(41)x+c R: int (a cos x+b sin x)/(c cos x+d sin x)dx= (ac+bd)/(c^(2)+d^(2))x+(ad-bc)/(c^(2)+d^(2))log|c cos x+d sin x |+k

    A
    Both A and R are true and R is the correct explanation of A
    B
    Both A and R are true and R is not correct explanation of A
    C
    A is true R is false
    D
    A is false but R is true.

  • int(1)/(2cos x+ 3 sin x+4)dx=

    A
    `(1)/(sqrt(3))Tan^(-1)[(1)/(sqrt(3))(2tanx//2+3)]+c`
    B
    `(2)/(sqrt(3))Tan^(-1)[(1)/(sqrt(3))(2tanx//2+3)]+c`
    C
    `(2)/(sqrt(3))Tan^(-1)[(1)/(sqrt(3))(2tanx//2-3)]+c`
    D
    none

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    int (3cos x-2sin x)/(4 sin x+5 cosx)dx=

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