Home
Class 12
MATHS
int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a)...

`int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx=` (a) `sqrt(x^2+1/(x^2)+1)+C` (b) `(sqrt(x^4+x^2+1))/(x^2)+C` (c) `(sqrt(x^4+x^2+1))/x+C` (d) none of these

A

`sqrt(x^(2)+(1)/(x^(2))+1)+C`

B

`(sqrt(x^(4)+x^(2)+1))/(x^(2))+C`

C

`(sqrt(x^(4)+x^(2)+1))/(x)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`I=int(x^(4)-1)/(x^(2)*xsqrt(x^(2)+(1)/(x^(2))+1))dx=int((x-(1)/(x^(3)))dx)/(sqrt(x^(2)+(1)/(x^(2))+1))`
Put `x^(2)+(1)/(x^(2))+1=t " or "2(x-(1)/(x^(3)))dx=dt`
` :. I=(1)/(2)int(dt)/(sqrt(t))=(1)/(2)*2sqrt(t)+C=sqrt(t)+C `
`=sqrt(x^(2)+(1)/(x^(2))+1)+C=(sqrt(x^(4)+x^(2)+1))/(x)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Exercises (Multiple Correct Answers Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Exercises (Linked Comprehension Type)|17 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 7.9|15 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

int(x^2-1)/(x^3sqrt(2x^4-2x^2+1))dx is equal to (a) (sqrt(2x^4-2x^2+1))/(x^3)+C (b) (sqrt(2x^4-2x^2+1))/x+C (c) (sqrt(2x^4-2x^2+1))/(x^2)+C (d) (sqrt(2x^4-2x^2+1))/(2x^2)+C

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

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

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

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

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

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

int(2xdx)/(sqrt(1-x^(2)-x^(4)))

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

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-EXERCISES (Single Correct Answer Type)
  1. int(x^3dx)/(sqrt(1+x^2))i se q u a lto 1/3sqrt(1+x^2)(2+x^2)+C 1/3...

    Text Solution

    |

  2. If I=int (dx)/((a^(2)-b^(2)x^(2))^(3//2)), then I equals

    Text Solution

    |

  3. int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (...

    Text Solution

    |

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

    Text Solution

    |

  5. int (1+2x^(6))/((1-x^(6))^(3//2))dx is equal to

    Text Solution

    |

  6. The integral int[2x^[12]+5x^9]/[x^5+x^3+1]^3.dx is equal to-

    Text Solution

    |

  7. If In=int( lnx)^n dx then In+nI(n-1)

    Text Solution

    |

  8. Let inte^x{f(x)-f^(prime)(x)}dx=varphi(x)dot Then inte^xf(x)dx is

    Text Solution

    |

  9. For x >1,int sin^(- 1)((2x)/(1+x^2))dx is equal to

    Text Solution

    |

  10. If int(xln(x+sqrt(1+x^2)))/(sqrt(1+x^2))dx =asqrt(1+x^2)ln(x+sqrt(1+x...

    Text Solution

    |

  11. Ifintxlog(1+1/x)dx=f(x)log(x+1)+g(x)x^2+A x+C , then f(x)=1/2x^2 (b) ...

    Text Solution

    |

  12. If I=inte^(-x)log(e^x+1)dx ,t h e nIe q u a l a+(e^(-x)+1)log(e^x+1)...

    Text Solution

    |

  13. Find the value of " int x sec^(2)x dx

    Text Solution

    |

  14. int x sinx sec^(3)x dx is equal to

    Text Solution

    |

  15. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

    Text Solution

    |

  16. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx is equal to (a)e^xtan(pi/4-x...

    Text Solution

    |

  17. int e^(x^4) (x^3) dx is equal to

    Text Solution

    |

  18. The value of integral inte^x(1/(sqrt(1+x^2))+(1-2x^2)/(sqrt((1+x^2)^5)...

    Text Solution

    |

  19. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

    Text Solution

    |

  20. int((x+2)/(x+4))^2 e^xdx is equal to

    Text Solution

    |