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int (1)/(x^(2)sqrt(1+x^(2)))dx=...

`int (1)/(x^(2)sqrt(1+x^(2)))dx=`

A

`-(sqrt(1+x^(2)))/(x)+c`

B

`(sqrt(1+x^(2)))/(x)+c`

C

`-(sqrt(1-x^(2)))/(x)+c`

D

none

Text Solution

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The correct Answer is:
A
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Knowledge Check

  • int (1)/((1x^(2))sqrt(1-x^(2)))dx

    A
    `-(1)/(sqrt(2))Tanh^(-1)((sqrt(1+x^(2)))/(sqrt(2)x))+c`
    B
    `(1)/(sqrt(2))Tanh^(-1)((sqrt(1+x^(2)))/(sqrt(2)x))+c`
    C
    `-(1)/(sqrt(2))Tanh^(-1)((sqrt(1-x^(2)))/(sqrt(2)x))+c`
    D
    none

  • int (1)/((x^(2)+9)sqrt(x^(2)-9))dx=

    A
    `(1)/(8sqrt(2))log|(sqrt(2)-x-sqrt(x^(2)-9))/(sqrt(2)x-sqrt(x^(2)-9))|+c`
    B
    `(1)/(18sqrt(2))log|(sqrt(2)+x-sqrt(x^(2)-9))/(sqrt(2)x-sqrt(x^(2)-9))|+c`
    C
    `(1)/(18sqrt(2))log|(sqrt(2)+x-sqrt(x^(2)+9))/(sqrt(2)x-sqrt(x^(2)-9))|-c`
    D
    none

  • int (1)/(x+sqrt(x^(2)+1))=dx

    A
    `(x)/(2)sqrt(x^(2)+1)+(1)/(2) Sinh^(-1)x-(x^(2))/(2)+c`
    B
    `(x)/(2)sqrt(x^(2)+1)-(1)/(2) Sinh^(-1)x-(x^(2))/(2)+c`
    C
    `(x)/(2)sqrt(x^(2)-1)+(1)/(2) Sinh^(-1)x-(x^(2))/(2)+c`
    D
    none

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