Home
Class 12
MATHS
Evaluate the following integrals: intc...

Evaluate the following integrals:
`intcos^(-1)((1-x^(2))/(1+x^(2)))dx`

Text Solution

Verified by Experts

The correct Answer is:
`2xtan^(-1)x-log(1+x^(2))+C`
Put `x=tant anddx=sec^(2)t" dt. Use"((1-tan^(2)t)/(1+tan^(2)t))=cos2t`.
Promotional Banner

Topper's Solved these Questions

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Objective Questions Ii|56 Videos

  • METHODS OF INTEGRATION

    RS AGGARWAL|Exercise Exercise 13B|34 Videos

  • MATRICES

    RS AGGARWAL|Exercise Exercise 5F|21 Videos

  • PROBABILITY

    RS AGGARWAL|Exercise Exercise 29 B|2 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integrals: inttan^(-1)((3x-x^(3))/(1-3x^(2)))dx

Evaluate the following integrals: intcos^(-1)(4x^(3)-3x)dx

Evaluate the following integrals: intcos^(-1)sqrt(x)dx

Evaluate the following integral: int_(0)^(1)cos^(-1)((1-x^(2))/(1+x^(2)))dx

Evaluate the following integrals: intcos^(3)(3x+5)dx

Evaluate the following integrals: int(sin^(-1)x)/(x^(2))dx

Evaluate the following integrals: inttan^(-1)((2x)/(1-x^(2)))dx

Evaluate the following integrals: int(x-(1)/(x))^(2)dx

Evaluate the following integrals: int(x-(1)/(x))^(2)dx

Evaluate the following integrals: inte^(x)(tan^(-1)x+(1)/(1+x^(2)))dx

RS AGGARWAL-METHODS OF INTEGRATION -Exercise 13C
  1. Evaluate the following integrals: intcos^(-1)sqrt(x)dx

    Text Solution

    |

  2. Evaluate the following integrals: intcos^(-1)(4x^(3)-3x)dx

    Text Solution

    |

  3. Evaluate the following integrals: intcos^(-1)((1-x^(2))/(1+x^(2)))dx

    Text Solution

    |

  4. Evaluate the following integrals: inttan^(-1)((2x)/(1-x^(2)))dx

    Text Solution

    |

  5. Evaluate the following integrals: inttan^(-1)((3x-x^(3))/(1-3x^(2)))...

    Text Solution

    |

  6. Evaluate the following integrals: int(sin^(-1)x)/(x^(2))dx

    Text Solution

    |

  7. Evaluate the following integrals: int(tanxsec^(2)x)/((1-tan^(2)x))dx

    Text Solution

    |

  8. Evaluate the following integrals: inte^(3x)sin4xdx

    Text Solution

    |

  9. Evaluate the following integrals: inte^(2x)sinxdx

    Text Solution

    |

  10. Evaluate the following integrals: inte^(2x)sinxcosxdx

    Text Solution

    |

  11. Evaluate the following integrals: inte^(2x)cos(3x+4)dx

    Text Solution

    |

  12. Evaluate the following integrals: inte^(-x)cosxdx

    Text Solution

    |

  13. Evaluate the following integrals: inte^(x)(sinx+cosx)dx

    Text Solution

    |

  14. Evaluate the following integrals: inte^(x)(cotx-"cosec"^(2)x)dx

    Text Solution

    |

  15. Evaluate the following integrals: inte^(x)secx(1+tanx)dx

    Text Solution

    |

  16. Evaluate the following integrals: inte^(x)(tan^(-1)x+(1)/(1+x^(2)))d...

    Text Solution

    |

  17. inte^(x)(cotx+logsinx)dx=?

    Text Solution

    |

  18. inte^x(tanx-logcosx)dx

    Text Solution

    |

  19. inte^(x)[secx+log(secx+tanx)]dx=?

    Text Solution

    |

  20. Evaluate the following integrals: inte^(x)((1+sinxcosx)/(cos^(2)x))d...

    Text Solution

    |