Home
Class 12
MATHS
If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^...

If `int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n` `f(x)` is an even function `f(x)` is a bounded function the range of `f(x)` is `(0,1)` `f(x)` has two points of extrema

Text Solution

Verified by Experts

The correct Answer is:
Option 1 2 3
Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE|Exercise Exercise (Numerical) & JEE Previous Year|11 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE|Exercise JEE Previous Year|20 Videos

Similar Questions

Explore conceptually related problems

If int f' (x) e^(x^(2)) dx = (x-1)e^(x^(2)) + c , then f (x) is

If int (e^x-1)/(e^x+1)dx=f(x)+C, then f(x) is equal to

If int f'(x) e^(x^(2))dx = (x-1)e^(x^(2))+c then f (x) is . . . . .

Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

If f(x)={x^2, for xgeq1x ,for x<0 ,t h e n fof(x) is given by

If int(xe^(x))/(sqrt(1+e^(x)))dx=f(x)sqrt(1+e^(x))-2logg(x)+C , then

Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n both f(x)a n dg(x) are odd functions f(x) is monotonic function f(x)=g(x) has no real roots int(f(x))/(g(x))dx=-1/x+3/(x^3)+c

"If " int e^(x^(3)+x^(2)-1)(3x^(4)+2x^(3)+2x)dx=f(x)+C, " then the value of " f(1)xxf(-1) " is"-.

For x >0,l e tf(x)=int_1^x(logt)/(1+t)dtdot Find the function f(x)+f(1/x) and find the value of f(e)+f(1/e)dot

CENGAGE-INTEGRALS-Solved Examples And Exercises
  1. Statement 1: For -1<a<4,int(dx)/(x^2+2(a-1)x+a+5) =lambdalog|g(x)|+c ...

    Text Solution

    |

  2. If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an e...

    Text Solution

    |

  3. Evaluate: for m in N , intx^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx...

    Text Solution

    |

  4. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

    Text Solution

    |

  5. I=int(dx)/((2a x-x^2)

    Text Solution

    |

  6. If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) ...

    Text Solution

    |

  7. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

    Text Solution

    |

  8. If l^(prime)(x) means logloglog x , the log being repeated r times, th...

    Text Solution

    |

  9. int(2sinx)/((3+sin2x)dxi se q u a lto 1/2ln|(2+sinx-cosx)/(2-sinx+co...

    Text Solution

    |

  10. Evaluate: int((x-1)e^x)/((x+1)^3)dx

    Text Solution

    |

  11. Evaluate int(dx)/(x^(2)(x^(4)+1)^((3)/(4))).

    Text Solution

    |

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

    Text Solution

    |

  13. IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s a. 1/2((sqrt(x^2-1...

    Text Solution

    |

  14. If I=int e^(-x) log(e^x+1) dx, then equal

    Text Solution

    |

  15. IfI(m , n)=intcos^m xsinn xdx , then 7I(4,3)-4I(3,2)" is equal to" (a...

    Text Solution

    |

  16. Evaluate int(sqrt(tan x)+sqrt(cot x))dx.

    Text Solution

    |

  17. If I=int sqrt((5-x)/(2+x)) dx, then equal

    Text Solution

    |

  18. Evaluate: int(1/(x3+x4)+(ln(1+x6)/(x3+sqrt(x)))dx

    Text Solution

    |

  19. Evaluate int(sqrt(tan x)+sqrt(cot x))dx.

    Text Solution

    |

  20. IfI=int(dx)/((a^2-b^2x^2)^(3/2)),t h e nIe q u a l (a)x/(a^2sqrt(a^2-...

    Text Solution

    |