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If x^2!=n pi-1, n in N. Then, the value ...

If `x^2!=n pi-1, n in N`. Then, the value of `int x sqrt((2sin(x^2+1)-sin2(x^2+1))/(2sin(x^2+1)+sin2(x^2+1)))dx` is equal to:

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

  • Let x^2 ne npi-1, n in N , then intxsqrt((2sin(x^2+1)-sin2(x^2+1))/(2sin(x^2+1)+sin2(x^2+1)))dx equals

    A
    `log|1/2sec(x^2+1)|+C`
    B
    `log|sec(1/2(x^2+1))|+C`
    C
    `1/2log|sec(x^2+1)|+C`
    D
    None of these

  • For x ^ 2 ne n pi + 1, n in N ( the set of natural numbers ), the integral int x sqrt ((2 sin (x ^ 2 - 1 ) - sin 2 (x ^ 2 - 1 ))/(2 sin ( x ^ 2 - 1 ) + sin2 (x ^ 2 - 1 ) )) dx is

    A
    `log _e | sec ((x ^ 2 - 1 )/ (2)) | + c `
    B
    ` (1)/(2) log _e | sec ( x ^ 2 - 1 ) | + c `
    C
    ` (1)/(2) log _e | sec ^ 2 ((x ^ 2 - 1 )/(2))| + c `
    D
    ` log _e | (1)/(2) sec ^ 2 (x ^ 2 - 1) | + c `

  • int_(-1)^(1)(x sin^2x)/(sqrt(1-x^2))dx is equal to

    A
    1
    B
    0
    C
    4
    D
    2

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