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

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

A

`sec ^(-1) ((x ^(2) +1 )/( sqrt2 x)) + c`

B

`(1)/(sqrt2) sec ^(-1) (( x ^(2) +1 )/( sqrt2 x )) +c`

C

`(1)/(sqrt2) sec ^(-1) ((x ^(2) +1 )/( sqrt2 x )) +c`

D

None of these

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The correct Answer is:
B
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DISHA PUBLICATION-INTEGRALS -EXERCISE-1 CONCEPT BUILDER
  1. Evaluate: int(x^3+x)/(x^4-9)\ dx

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  2. int (dx)/( sin x ( 3 cos ^(2) x)) is equal to

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

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  4. int ( x ^(3))/( (x ^(2) + 1) (x ^(2) + 4 ))dx is equal to

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  5. int(e^(x)(1+x))/(cos^(2)(e^(x)x))dx equal to

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  6. If int (3x+4)/(x^3-2x-4) \ dx = log|x-2| + k logf(x) + c, then (i) f...

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  7. int (27 e ^(9x) + e ^( 12 x )) ^(1//3) dx is equal to

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  8. Evaluate: int(sinx)/(sin4x)dx

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  9. int(1)/(x^(2)(x^(4)+1)^(3//4))dx is equal to

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  10. int sin 2x. Logcos x dx is equal to

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  11. If int (e ^(x) (1+ sin x )dx)/( 1+ cos x ) = e ^(x) f (x) + C, then f ...

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  12. If a (n) = int(0) ^( (pi)/(2)) (sin^(2) nx)/( sin x) dx then a (2) ...

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  13. Let I=overset(1)underset(0)int (sin x)/(sqrt(x))dx andI=overset(1)unde...

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  14. overset(pi//2)underset(-pi//2)int (|x|)/(8 cos^(2)2x+1)dxhas the value

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  15. If underset(0)overset(1)int e^(x^(2))(x-alpha)dx=0 then

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  16. The value of the integral int(0) ^(pi) cos 2 x log (e) sin x dx is

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  17. If int(1/2)^2 1/x cosec^(101)(x-1/x)dx=k then the value of k is :

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  18. The value of int-pi^pi cos^2x/[1+a^x].dx,a>0 is

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  19. The value of int(1)^(e^(37))(pi sin(pi log x))/(x)dx is ………….

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  20. Evaluate int (0)^(pi)(x)/(1+ cos^(2)x)dx.

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