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int (sqrt(x^(2)+1)[log(x^(2)+1)-2 logx])...

`int (sqrt(x^(2)+1)[log(x^(2)+1)-2 logx])/(x^(4))dx=`

A

`((x^(2)+1)^(3//2))/(9x^(3))[2+3log(1+(1)/(x^(2)))]+c`

B

`((x^(2)+1)^(3//2))/(9x^(3))[1-2 log(1+(1)/(x^(2)))]+c`

C

`((x^(2)+1)^(3//2))/(9x^(3))[2-3 log(1+(1)/(x^(2)))]+c`

D

`((x^(2)+1)^(3//2))/(9x^(3))[2+3 log(1-(1)/(x^(2)))]+c`

Text Solution

Verified by Experts

The correct Answer is:
C
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Knowledge Check

  • int (x)/(sqrt(x^(2)+1))dx=

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

  • int (sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(4)))dx=

    A
    `log(x+sqrt(1+x^(2)))+ Sin^(-1)x+c`
    B
    `Sinh^(-1)x-Sin^(-1)x+c`
    C
    `Cos^(-1)-Sin^(-1)x+c`
    D
    `Tan^(-1)x+sin^(-1)x+c`

  • int log (x+sqrt(x^(2)-1))dx=

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

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    int sqrt((x - 1)/(x -2)) dx =

    int (x)/(sqrt(1- x^(2)) cos^(2) sqrt(1 - x^(2))) dx =

    int (1)/(log x)-(1)/((log x)^(2))dx=

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