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int(dx)/(a^2-b^2x^2)=...

`int(dx)/(a^2-b^2x^2)=`

A

`(1)/(ab)log|(a-bx)/(a+bx)|+c`

B

`(1)/(ab)log|(a+bx)/(a-bx)|+c`

C

`(1)/(2ab)log|(a-bx)/(a+bx)|+c`

D

`(1)/(2ab)log|(a+bx)/(a-bx)|+c`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • int(dx)/(x^(2)-2x+2)=

    A
    `1/2tan^(-1)(x-1)+c`
    B
    `tan^(-1)(x-1)+c`
    C
    `1/2logabs((x+sqrt(2))/(x-sqrt(2)))+c`
    D
    `1/2logabs((x-sqrt(2))/(x+sqrt(2)))+c`

  • The integral int(dx)/((a^(2)-b^(2)x^(2))^(3//2)) equals

    A
    `(x)/(sqrt(a^(2)-b^(2)x^(2)))+C`
    B
    `(x)/(a^2(sqrt(a^(2)-b^(2)x^(2))))+C`
    C
    `(ax)/(sqrt(a^(2)-b^(2)x^(2)))+C`
    D
    `(1)/(a^(2)sqrt(a^(2)-b^(2)x^(2)))+C`

  • int(dx)/(sqrt(a^2-b^2x^2))=

    A
    `(1)/(b)sin^(-1)((bx)/(a))+c`
    B
    `(1)/(b)sin^(-1)((ax)/(b))+c`
    C
    `(1)/(a)sin^(-1)((bx)/(a))+c`
    D
    `(1)/(a)sin^(-1)((ax)/(b))+c`

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