Home
Class 12
MATHS
The value of int1^e (1+x^2 In x)/(x+x^2 ...

The value of `int_1^e (1+x^2 In x)/(x+x^2 In x) dx` is equal (a) `In (1+e)e+In(1+e)` (b) `e-In(1+e)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

The value of int_(1//e )^(e )(|log x|)/(x^(2))dx , is

int(x e^x)/((1+x)^2)dx is equal to

int_(0)^(1) ( dx)/( e^(x) + e^(-x)) is equal to

int_(0)^(1) ( dx)/( e^(x) + e^(-x)) is equal to

int_- 1^1(e^(-1/ x))/(x^2(1+e^(-2/ x)))dx is equal to :

The value of int_1^e((x/e)^(2x)+(e/x)^x)log_ex dx is equal to (A) e-1/(2e^2)-1/2 (B) e-1/(2e^2)+1/2 (C) e^3-1/(2e^2)-1/2 (D) none of these

The value of int_(log1//2)^(log2)sin{(e^(x)-1)/(e^(x)+1)}dx is equal to

The value of int_0^1e^(x^2-x) dx is (a) 1 (c) > e^(-1/4) (d) < e^(-1/4)

int_(1)^(e) (e^(x) (1+xlog x))/(x) dx

The value of int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b) tan^(-1)e (c) tan^(-1)(1/e) (d) none of these

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. int0^oo(x dx)/((1+x)(1+x^2)) is equal to (A) pi/4 (B) pi/2 (C) p...

    Text Solution

    |

  2. int0^oo(dx)/([x+sqrt(x^2+1)]^3)i se q u a lto 3/8 (b) 1/8 (c) -3/8 ...

    Text Solution

    |

  3. The value of int1^e (1+x^2 In x)/(x+x^2 In x) dx is equal (a) In (1+...

    Text Solution

    |

  4. The value of integral int0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be...

    Text Solution

    |

  5. Ifint0^oo(x^2dx)/((x^2+a^2)(x^2+b^2)(x^2+c^2)) =pi/(2(a+b)(b+c)(c+a...

    Text Solution

    |

  6. The value of the integral int0^1(dx)/(x^2+2xcosalpha+1) is equal to ...

    Text Solution

    |

  7. Determine a positive integer nlt=5 such that int0^1e^x(x-1)^n=16-6e

    Text Solution

    |

  8. Let f be a continuous function on [a ,b]dot Prove that there exists a ...

    Text Solution

    |

  9. If f(x)={(1-|x| ,, |x|lt=1),(0 ,, |x|>1):} and g(x)=f(x-1)+f(x+1), th...

    Text Solution

    |

  10. Evaluate: int0^(1)sin^(-1)((2x)/(1+x^2))dx

    Text Solution

    |

  11. Evaluate: int0^(pi/4)(tan^(-1)((2cos^2theta)/(2-sin2theta)))sec^2theta...

    Text Solution

    |

  12. L e t \ f(n)=1+1/2+1/3+...+1/n. Then show that f(n)=int0^(pi/2)cot(the...

    Text Solution

    |

  13. Let f(x) be a continuous function AAx in R , except at x=0, such that...

    Text Solution

    |

  14. If f(x)=(sinx)/xAAx in (0,pi], prove that pi/2int0^(pi/2)f(x)f(pi/2-x)...

    Text Solution

    |

  15. Determine a positive integer n such that int0^(pi/2)x^nsinx dx=3/4(pi^...

    Text Solution

    |

  16. f,g,h are continuous in [0,1],f(a-x)=f(x),g(a-x)=-g(x),3h(x)-4h(a-x)=5...

    Text Solution

    |

  17. If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int0^2f(2-...

    Text Solution

    |

  18. Let f(x) = (1 - x)^2 sin^2 x + x^2 for all x ∈ R, and let g(x) = ∫((2...

    Text Solution

    |

  19. Evaluate: int3^10[log[x]]dx

    Text Solution

    |

  20. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |