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Let I = int (e^x)/(e^(4x)+e^(2x)+1)dx, ...

Let ` I = int (e^x)/(e^(4x)+e^(2x)+1)dx, J=int (e^(-x))/(e^(-4x)+e^(-2x)+1)dx`. Then , for an arbitrary constant c, the value of J-1 euqals :

A

`(1)/(2)log((e^(4x)-e^(2x)+1)/(e^(4x+e^(x)+1)))+c`

B

`(1)/(2)log((e^(2x)+e^(x)+1)/(e^(2x)-e^(x)+1))+c`

C

`(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+c`

D

`(1)/(2)log ((e^(4x)+e^(2x)+1)/(e^(4x)-e^(2x)+1))+c`.

Text Solution

Verified by Experts

The correct Answer is:
C
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MODERN PUBLICATION-INDEFINITE INTEGERALS-MCQs Multiple Choice Questions Level-II
  1. int 1/(x^(2)(x^(4)+1)^(3//4)) dx is equal to .

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  2. Integral of f(x)=sqrt(1+x^(2)) w.r.t x^(2) is :

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  3. Find the value of int(d(x^2+1))/(sqrt((x^2+2))).

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  4. Let f(x)=int (x^2)/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0,Then f(1) is ...

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  5. int e^(tan-1)x((1+x+x^2)/(1+x^2))dx equals :

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  6. If int(1)/((x^2+1)(x^2+4))dx=a tan^(-1). x+b tan^(-1).(x)/(2)+c, then ...

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  7. If int sqrt(1+sec x)dx=k sin^(-1) (f(x))+c, then:

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  8. If f(x)=(x+2)/(2x+3), then intsqrt((f(x))/(x^2))dxequals : (1)/(sqrt(2...

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  9. int sin^(-3//2) x sin^(-1//2) (x+alpha)dx = -2 cosec alphasqrt(f(x))+c...

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  10. If int (sqrt(1+3sqrt(x)))/(x^(2//3))dx=2f(x)^(3//2)+c, then f(x)equals...

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  11. int e^(tan^(-1)x) ((1+x+x^2)/(1+x^2))dx

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  12. int(sqrt(tanx)+sqrt(cotx))dx is equal to

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  13. int(2^x)/(sqrt(1-4^x))dx=ksin^(- 1)2^x+c, then k =

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  14. intx^(2)e^(x^(3))dx is equal to :

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  15. int e^(e^(e^(x)))e^(e^(x))dx is equal to :

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  16. int{(logx-1)/(1+(logx)^(2))}^(2) dx is equal to

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  17. The value of sqrt(2)int(sinx)/(sin(x-(pi)/(4)))dx is :

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  18. int ((x^2-1)x)/(x^4sqrt(2x^4-2x^2+1))dx is equal to :

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  19. Let f(x)=(x)/((1+x^n)^((1)/(n)) for n ge 2 and g(x)=("fofo……………………..of...

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  20. Let I = int (e^x)/(e^(4x)+e^(2x)+1)dx, J=int (e^(-x))/(e^(-4x)+e^(-2x...

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