Home
Class 12
MATHS
i=int(e^(x))/((x+2)){1+(x+2)log(x+2)}dx=...

`i=int(e^(x))/((x+2)){1+(x+2)log(x+2)}dx=`

A

`e^(x).log(x+2)+c`

B

`e^(x)//(x+2)+c`

C

`e^(x)(x+2)+c`

D

`e^(x)(x-2)+c`

Text Solution

Verified by Experts

The correct Answer is:
A
`1= int e^(x).[(1)/(underset(g'(x))(ubrace(x+2)))+underset(g(x))(ubrace(log(x+2))]]dx`
`rArr 1= e^(x). g(x) =e^(x). log (x+2) c`
Promotional Banner

Topper's Solved these Questions

  • MOCK TEST 3

    CAREER POINT|Exercise MATHS|30 Videos

  • MOCK TEST 5

    CAREER POINT|Exercise Part (C) (MATHS)|30 Videos

Similar Questions

Explore conceptually related problems

I=int(e^(2x)-1)/(e^(2x))dx

int(e^(ln x))/(1+x^(2))dx

Evaluate: int(e^(x))/(x){x(log x)^(2)+2log x}dx

I=int(log(x^2))/(x)dx

1) int x log x^(2)dx

int_(e^(-1))^(e^(2))|(ln x)/(x)|dx

" (2) "int e^(x log e)dx

Statement -1 : If I_(1)=int(e^(x))/(e^(4x)+e^(2x)+1)dx and I_(2)=int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx , then I_(2)-I_(1)=(1)/(2)log((e^(2x)-e^(x)+1)/(e^(2x)+e^(x)+1))+C where C is an arbitrary constant. Statement -2 : A primitive of f(x) =(x^(2)-1)/(x^(4)+x^(2)+1) is (1)/(2)log((x^(2)-x+1)/(x^(2)+x+1)) .

int(1)/(x(log x)^(2))dx

CAREER POINT-MOCK TEST 4-MATHS
  1. The area bounded by the curves y= "sin" x, y= cos x and y-axis in 1 qu...

    Text Solution

    |

  2. The solution of the DE (dy )/(dx) + sqrt ((1 -y ^(2))/( 1- x ^(2))...

    Text Solution

    |

  3. A variable circle having fixed radius 'a' passes through origin and me...

    Text Solution

    |

  4. The chord A B of the parabola y^2=4a x cuts the axis of the parabola a...

    Text Solution

    |

  5. If tangents are drawn to the ellipse x^2+2y^2=2, then the locus of the...

    Text Solution

    |

  6. f(x) = ("tan" x^(5))e^(x^(3)"sgn"x^(7)) " is " -

    Text Solution

    |

  7. "if y"="cos"^(-1)((5"cos" x-12 "sin"x)/(13)), where x in (0,(pi)/(2)...

    Text Solution

    |

  8. lim(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-

    Text Solution

    |

  9. If veca,vecb,vecc are three mutually perpendicular vectors, then the v...

    Text Solution

    |

  10. A straight line moves so that the sum of the reciprocals of its interc...

    Text Solution

    |

  11. The points (1,1), (0, "sec"^(2) 0), ("cosec"^(2) 0,0 ) are collinear f...

    Text Solution

    |

  12. The equation of a line which passes through point A(1,0,-1) and perper...

    Text Solution

    |

  13. The curve y=ax^(3)+bx^(2)+cx is inclined by 45^(@) to x-axis at origi...

    Text Solution

    |

  14. If x^(2) +ax - 3x-(a+2) = 0 has real and distinct roots, then minimum ...

    Text Solution

    |

  15. i=int(e^(x))/((x+2)){1+(x+2)log(x+2)}dx=

    Text Solution

    |

  16. If R is a relation on N as R= {(1+ x, 1+x^2): x <= 5, X in N} which of...

    Text Solution

    |

  17. Cosnsider the system of equation a(1)x+b(1)y+c(1)z=0, a(2)x+b(2)y+c(...

    Text Solution

    |

  18. A sample of 35 observations has the means 80 and SD. As 4. A second sa...

    Text Solution

    |

  19. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)...

    Text Solution

    |

  20. Given A=[(1,1,1),(2,4,1),(2,3,1)], B=[(2,3),(3,4)]. Find P such tha...

    Text Solution

    |