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int(dx)/(cosx+sqrt3 sinx)dx is equal to...

`int(dx)/(cosx+sqrt3 sinx)dx` is equal to

A

`1/2logtan(x/2+pi/12)+C`

B

`1/2logtan(x/2-pi/12)+C`

C

`logtan(x/2+pi/12)+C`

D

`logtan(x/2-pi/12)+C`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • int (dx)/(cosx+sqrt3 "sin" x) is equal to

    A
    `1/2"log tan"(x/2 + pi/12)+C`
    B
    `1/2"log tan"(x/2 - pi/12)+C`
    C
    `"log tan"(x/2 + pi/12)+C`
    D
    `"log tan"(x/2 - pi/12)+C`

  • int(cosx)/(sqrt(1+sinx))dx is equal to

    A
    `sin.(x)/(2)-cos.(x)/(2)+C`
    B
    `sin.(x)/(2)+cos.(x)/(2)+C`
    C
    `2[sin.(x)/(2)-cos.(x)/(2)]+C`
    D
    `2[sin.(x)/(2)+cos.(x)/(2)]+C`

  • int(1)/(cosx-sinx)dx is equal to

    A
    `(1)/(sqrt(2))log|tan((x)/(2)+(3pi)/(8))|+C`
    B
    `(1)/(sqrt(2))log|"cot"(x)/(2)|+C`
    C
    `(1)/(sqrt(2))log|tan((x)/(2)-(3pi)/(8))|+C`
    D
    `(1)/(sqrt(2))log|tan((x)/(2)-(pi)/(8))|+C`

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