Home
Class 12
MATHS
Evaluate int(2)^(3)(2x^(5)+x^(4)-2x^(3)+...

Evaluate `int_(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))dx`

Text Solution

Verified by Experts

The correct Answer is:
`[(1)/(2)(log 6-(1)/(5))]`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRALS

    AAKASH SERIES|Exercise Exercise - 2.7 (Level-2)|21 Videos

  • COMPLEX NUMBERS

    AAKASH SERIES|Exercise PRACTICE EXERCISE|93 Videos

  • DEMOIVRE'S THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|64 Videos

Similar Questions

Explore conceptually related problems

int_(2)^(3) (2x)/(1+x^(2))dx

Evaluate int(x^(2))/(x^(4)+x^(2)+1)dx

int_(-1)^(1) (17x^(5)-x^(4)+29 x^(3) -31 x +1)/(x^(2)+1)dx=

int_(2)^(3) (2x)(1+x^2) dx

Evaluate int_(1)^(2)((x+1)^(3))/(x^(2))dx

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

Evaluate int_(1)^(2) ((x+1)^(3))/(x^(2)) dx

Evaluate int_(1)^(4) x sqrt(x^(2)-1) dx

AAKASH SERIES-DEFINITE INTEGRALS-Exercise (Level-2)
  1. Evaluate int(2)^(3)(2x^(5)+x^(4)-2x^(3)+2x^(2)+1)/((x^(2)+1)(x^(4)-1))...

    Text Solution

    |

  2. Show that int(0)^(pi//4)(x^(2))/((x sin x + cos x)^(2))dx - (4-pi)/(4+...

    Text Solution

    |

  3. Show that int(1)^(2)(x+(1)/(x))^(3//2)((x^(2)-1)/(x^(2)))dx = ((5)/(2)...

    Text Solution

    |

  4. Show that int(2)^(2sqrt(3)) x^(3)(x^(2)-3)^(3//2)dx = (16012)/(35)

    Text Solution

    |

  5. Prove that int(0)^(oo) (dx)/((x^(2)+a^(2))(x^(2)+b^(2)))=(pi)/(2ab(a+b...

    Text Solution

    |

  6. Prove that int(a)^(oo) (dx)/(x^(4)sqrt(a^(2) + x^(2)))=(2-sqrt(2))/(3a...

    Text Solution

    |

  7. Prove that int(0)^(pi//2) "cosec" (x-(pi)/(3))"cosec"(x-(pi)/(6)) dx =...

    Text Solution

    |

  8. Show that int(0)^(oo) (dx)/([x+sqrt(x^(2)+1)]^(3)) = (3)/(8)

    Text Solution

    |

  9. Show that int(0)^(pi)cos (2 cot^(-1) (sqrt((1-x)/(1+x))))dx = -(1)/(2)

    Text Solution

    |

  10. Show that int(0)^(pi//2) (dx)/(3+4 six) = (1)/(sqrt(7)) log((4+sqrt(7)...

    Text Solution

    |

  11. If int(log 2)^(x) (dy)/(sqrt(e^(y) -1)) = (pi)/(6), prove that x = log...

    Text Solution

    |

  12. If int(log 2)^(x)(1)/(e^(x)-1)dx = log""(3)/(2), show that x = log 4

    Text Solution

    |

  13. Show that int(0)^(1//2)(x sin^(-1)x)/(sqrt(1-x^(2)))dx = (1)/(2)-(sqrt...

    Text Solution

    |

  14. Prove that int(0)^(pi//2) tan^(-1)(sin x) .sin 2x = (pi)/(2)-1

    Text Solution

    |

  15. Show that (a) int(e)^(e^(2))(1)/(log x)dx = int(1)^(2)(e^(x))/(x)dx ...

    Text Solution

    |

  16. Prove that int(0)^(1) log(sqrt(1-x)+sqrt(1+x))dx = (1)/(2) log 2 + (pi...

    Text Solution

    |

  17. Show that int(0)^(pi//4) x cos x cos 3 x dx = (pi-3)/(16)

    Text Solution

    |

  18. Prove that int(0)^(oo) e^(-2x)(sin 2x + cos 2 x) dx = (1)/(2)

    Text Solution

    |

  19. Show that int(0)^(pi//2) (cos x)/((1+sin x)(2+sin x)) dx = log((4)/(3...

    Text Solution

    |

  20. Show that int(1)^(7thsqrt(2))(1)/(x(2x^(7) + 1))dx=(1)/(7) log((6)/(5)...

    Text Solution

    |