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For x^(2) ne npi + 1, n in N(the set of ...

For `x^(2) ne npi + 1, n in N`(the set of natural numbers), the integral `int x sqrt((2sin(x^(2)-1)-sin2(x^(2)-1))/(2sin(x^(2)-1)+sin2(x^(2)-1)))dx` is equal to (where C is a constant of integration)

A

`log_eabs((sec.(x^2-1)/2))+c`

B

`log_eabs(1/2sec^2.(x^2-1))+c`

C

`1/2log_eabs(sec^2.((x^2-1)/2))+c`

D

`1/2log_eabs(sec.(x^2-1))+c`

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • sin^(-1)(2cos^(2)x-1)+cos^(-1)(1-2sin^(2)x)=

    A
    `(pi)/(2)`
    B
    `(pi)/(3)`
    C
    `(pi)/(4)`
    D
    `(pi)/(6)`

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