Home
Class 12
MATHS
Evaluate: int(x^2-1)/((x^4+3x^2+1)tan^(-...

Evaluate: `int(x^2-1)/((x^4+3x^2+1)tan^(-1)(x+1/x))dx`

Text Solution

Verified by Experts

The correct Answer is:
`I="In" | "arc" tan t| + C = "In" | "arc" tan ( x+ (1)/( x) ) | +C`.
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION

    IA MARON|Exercise 4.3. Integration by Parts|28 Videos

  • INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION

    IA MARON|Exercise 4.4. Reduction Formulas|2 Videos

  • INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION

    IA MARON|Exercise 4.4. Reduction Formulas|2 Videos

  • IMPROPER INTEGRALS

    IA MARON|Exercise 8.4 ADDITIONAL PROBLEMS|1 Videos

  • INTRODUCTION OF MATHEMATICAL ANALYSIS

    IA MARON|Exercise Additional Problems|34 Videos
IA MARON-INDEFINITE INTEGRALS, BASIC METHODS OF INTEGRATION-4.2. Integration by Substitution
  1. I= int (dx)/( 1+ e^( x) )

    Text Solution

    |

  2. I= int ( x^2 + 3) /( sqrt ( 2x -5)^(3) ) dx.

    Text Solution

    |

  3. Evaluate: int(x^2-1)/((x^4+3x^2+1)tan^(-1)(x+1/x))dx

    Text Solution

    |

  4. I= int ( sqrt( alpha^(2) - x^(2) ) )/( x^4) dx.

    Text Solution

    |

  5. I= int ( dx)/( a^(2) sin^(2) x + b^(2) cos^(2) x) .

    Text Solution

    |

  6. I= int root(3) ( 1+ 3 sin x) cos x dx.

    Text Solution

    |

  7. I= int ( sin x dx)/( sqrt( cos x) ).

    Text Solution

    |

  8. I= int ( dx)/( ("arc" cos x)^(5) sqrt(1-x^2) ).

    Text Solution

    |

  9. I= int ( x^2 + 1) /( root( 3) ( x^(3) + 3x + 1) )d x.

    Text Solution

    |

  10. I= int ( sin 2 x)/( 1+ sin^(2) x) dx.

    Text Solution

    |

  11. I= int ( 1+ "In" x)/( 3+ x "In" x) dx.

    Text Solution

    |

  12. Evaluate the following integrals : (a) int ( root( 3) (1+ "In" x) )/...

    Text Solution

    |

  13. Evaluate the following integrals : (b) int ( dx)/( x "In" x) ,

    Text Solution

    |

  14. Evaluate the following integrals : (c ) int ( xdx)/( sqrt( 3-x^4) ),

    Text Solution

    |

  15. Evaluate the following integrals : (d) int ( x^( n-1) )/( x^( 2n) + ...

    Text Solution

    |

  16. What is int (sin sqrtx)/(sqrtx) dx equal to ?

    Text Solution

    |

  17. Evaluate the following integrals : int ("In" x + (1)/( "In" x) ) (dx...

    Text Solution

    |

  18. Find the following integrals : (a) int x^(2) root( 3) ( 1-x) dx,

    Text Solution

    |

  19. Find the following integrals : (b) int ("In" x dx)/( x sqrt (1+ "In"...

    Text Solution

    |

  20. Find the following integrals : (c ) int cos^(5) x sqrt( sin x) dx,

    Text Solution

    |