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int (dx)/(sin(x-a)sin(x-b)=......+C...

`int (dx)/(sin(x-a)sin(x-b)`=`......+C`

A

`sin(b-a)log|(sin(x-b))/(sin(x-b))|`

B

`"cosec"(b-a)log|(sin(x-b))/(sin(x-b))|`

C

`"cosec"(b-a)log|(sin(x-b))/(sin(x-a))|`

D

`sin(b-a)log|(sin(x-a))/(sin(x-b))|`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • int (dx)/(sin^(2)x cos^(2)

    A
    `tan x+cotx+c`
    B
    `tanx-cotx+c`
    C
    `tan x cot x+c`
    D
    `tan x-cot 2x+c`

  • int(sin 2x)/(sin5x*sin3x)dx=.....+c

    A
    `log|sin3x|-log|sin5x|`
    B
    `(1)/(3)log|sinx3x|+(1)/(5)|sin 5x|`
    C
    `(1)/(3)log|sinx3x|-(1)/(5)|sin 5x|`
    D
    `3 log|sin3x|-5(1)/(5)log|sin 5x|`

  • inte^(4x)sin3xdx=......+c

    A
    `(e^(4x))/(25)(sinx+cosx)`
    B
    `(e^(4x))/(25)(4sin3x-3cos3x)`
    C
    `(e^(4x))/(5)(4sin3x-3cos3x)`
    D
    `(e^(4x))/(25)(4sin3x-3cos3x)`

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