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If l^r(x) means logloglog.......x being ...

If `l^r(x)` means `logloglog.......x` being repeated `r` times, then `int [ (x l(x) l^2(x) l^3(x) .... l^r (x)]^(-1) dx` is equal to :

A

`l^(r+1)(x)+C`

B

`(l^(r+1)(x))/(r+1)+C`

C

`l^(r)(x)+C`

D

non of these

Text Solution

Verified by Experts

The correct Answer is:
A
Putting `l^(r+1)(x)=t`
and `(1)/(xl(x)l^(2)(x) ...l^(r)(x))dx=dt,` we get
`int(dx)/(xl^(2)(x)l^(3)(x) ...l^(r)(x))=int 1 dt=t+C=l^(r+1)(x)+C`
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CENGAGE ENGLISH-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
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  3. If l^r(x) means logloglog.......x being repeated r times, then int [ (...

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  4. Find int[sqrt(cotx)+sqrt(tanx)]dx

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  5. If I= int (sin 2x)/((3+4cosx)^(3))dx, then I equals

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  6. int("In"((x-1)/(x+1)))/(x^(2)-1)dx is equal to

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

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  9. int(sqrt(x^2+10 x+24))/(x+5)dx is equal to

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  10. The value of int(1+logx)/(sqrt((x^(x))^(2)-1))dx " is "

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  11. "If "int x^(5)(1+x^(3))^(2//3)dx=A(1+x^(3))^(8//3)+B(1+x^(3))^(5//3)+c...

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  12. int(sin2x)/(sin^4x+cos^4x)d x

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  13. int(x+2)/((x^(2)+3x+3)sqrt(x+1))dx " is equal to"

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  14. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (x+2A...

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  15. int(cos2x)/((e^(-x)+cosx)sqrt(1+sin2x))dx,x in(0,(pi)/(2)) is equal t...

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  16. int(cos4x-1)/(cotx-tanx)dx is equal to

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  17. If int(dx)/(x^2(x^n+1)^((n-1)/n))=-(f(x))^(1/n)+C then f(x) is (...

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  18. int sqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to

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  19. intx((lna^(x/2)/(3a^((5x)/2)b^(3x))+(lnb^b^x)/(2a^(2x)b^(4x)))dx(w h e...

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  20. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c (b...

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