Home
Class 12
MATHS
int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx ...

`int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx` equals

A

`(1)/(2)ln.(x)/(lnx)-(1)/(4)ln(ln^(2)x-x^(2))+C`

B

`(1)/(4)ln((lnx-x)/(lnx+x))-(1)/(2)tan^(-1)((lnx)/(x))+C`

C

`(1)/(4)ln((lnx-x)/(lnx+x))+(1)/(2)tan^(-1)((lnx)/(x))+C`

D

`(1)/(4)(ln((lnx-x)/(lnx+x))+tan^(-1)((lnx)/(x)))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx`
`=int(1-logx)/(x(((logx)/(x))^(4)-1))dx`
Put `(logx)/(x)=t rArr (1-logx)/(x^(2))=dt`
`therefore" "I=int(dt)/((t^(4)-1))=int(dt)/((t^(2)+1)(t^(2)-1))`
`=(1)/(2)int((t^(2)+1)-(t^(2)-1))/((t^(2)+1)(t^(2)-1))dt`
`=(1)/(2)(int(dt)/(t^(2)-1)-int(dt)/(t^(2)+1))=(1)/(2)((1)/(2)ln(t-1)/(t+1)-tan^(-1)t)`
`=(1)/(4)ln((lnx-x)/(lnx+x))-(1)/(2)tan^(-1)((lnx)/(x))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int(e^(6logx)-x^(5))/(e^(4logx)-x^(3))dx

int(dx)/(x((logx)^(2)+1)) equals

inte^(-logx)dx=?

The integral int_(2)(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx is equal to

int(1)/(x(logx)log(logx))dx=

int(e^(7logx)-e^(6logx))/(e^(6logx)-e^(5logx))dx is:

Evaluate int_(1)^(2)(1)/(x(1+logx)^(2))dx .

Evaluate int((log x-1)/(1+(logx)^(2)))^(2)dx

Evaluate: int(log(logx)+1/((logx)^2))dx

The value of int_(0)^(oo)(logx)/(a^(2)+x^(2))dx is