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

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

A

`(1)/(4) log_(e)|(1-sqrt(1-x^(4)))/(1+sqrt(1-x^(4)))|+(1)/(2)sin^(-1)(x^(2))+C`

B

`(1)/(2) log_(e)|(1-sqrt(1-x^(4)))/(1+sqrt(1-x^(4)))|+(1)/(2)cos^(-1)(x^(2))+C`

C

`(1)/(2) log_(e)|(1-sqrt(1-x^(4)))/(1+sqrt(1-x^(4)))|+sin^(-1)(x^(2))+C`

D

` log_(e)|(1-sqrt(1-x^(4)))/(1+sqrt(1-x^(4)))|+(1)/(2)cos^(-1)(x^(2))+C`

Text Solution

Verified by Experts

The correct Answer is:
A
`int sqrt((x^(2)+1)/(x^(2)(1-x^(2))))dx=int sqrt((1+x^(2))/(x^(2)(1-x^(2)))) xx(sqrt(1+x^(2)))/(sqrt(1+x^(2)))dx`
`=int(1+x^(2))/(xsqrt(1-x^(4)))dx`
`=int(1)/(xsqrt(1-x^(4)))dx+int (x)/(sqrt(1-x^(4)))dx`
`=(1)/(4) log_(e)|(1-sqrt(1-x^(4)))/(1+sqrt(1-x^(4)))|+(1)/(2)sin^(-1)(x^(2))+c`
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CENGAGE-INDEFINITE INTEGRATION-Exercise (Single)
  1. int("In"((x-1)/(x+1)))/(x^(2)-1)dx is equal to

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  2. int sqrt(e^(x)-1)dx is equal to

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

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

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

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  6. "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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  7. int(sin2x)/(sin^4x+cos^4x)d x

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

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  9. int(sec xdx)/(sqrt(sin(2x+A)+sinA)) " is equal to "

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

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

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

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

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

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  15. int(3+2cosx)/((2+3cosx)^(2))dx is equal to

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  16. "If " (d)/(dx)f(x)=f'(x), " then " int(xf'(x)-2f(x))/(sqrt(x^(4)f(x)))...

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  17. The value of the integral int((1-costheta)^(2/7))/((1+costheta)^(9/7))...

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  18. If int(dx)/(sqrt(sin^(3)xcos^(5)x))=a sqrt(cot x)+bsqrt(tan^(3)x)+c, t...

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  19. "I f"int(dx)/(cos^3xsqrt(sin2x))=a(tan^2x+b)sqrt(tanx)+c

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  20. If int(dx)/((x+2)(x^(2)+1)) = alog|1+x^(2)|+btan^(-1)x+ 1/5log|x+2|+C,...

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