Home
Class 12
MATHS
"The integral " int(1+x-(1)/(x))e^(x+(1)...

`"The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "`

A

`(x+1)e^(x+(1)/(x))+C`

B

`-xe^(x+(1)/(x))+C`

C

`(x-1)e^(x+(1)/(x))+C`

D

`xe^(x+(1)/(x))+C`

Text Solution

Verified by Experts

The correct Answer is:
d
We have , `int(1+x-(1)/(x))e^(x+(1)/(x))dx`
`=inte^(x+(1)/(x))dx+intunderset(I)(x) e^(x+(1)/(x))(1-(1)/(x^(2)))dx`
`=inte^(x+(1)/(x))dx+xe^(x+(1)/(x))-inte^(x+(1)/(x))dx+C=xe^(x+(1)/(x))+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|3 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|61 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The value of the integral inte^(x^(2)+(1)/(x))(2x^(2)-(1)/(x)+1)dx is equal to (where C is the constant of integration)

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

int("In"((x-1)/(x+1)))/(x^(2)-1)dx is equal to

The integral int_(-1/2)^(1/2) ([x]+1n((1+x)/(1-x)))dx is equal to (where [.] represents the greatest integer function)

The integral int_(1)^(e){(x/e)^(2x)-(e/x)^x}log_exdx is equal to

The value of the integral int_(-1)^(1)(dx)/((1+x^(2))(1+e^(x)) is equal to

The integral int_(-1)^(1) (|x+2|)/(x+2)dx is equal to

The integral int(2x^(3)-1)/(x^(4)+x)dx is equal to : (Here C is a constant of integration)

int(1+x-x^(- 1))e^(x+x^(-1))dx=

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

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
  1. At present, a firm is manufacturing 2000 items. It is estimated tha...

    Text Solution

    |

  2. "If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "

    Text Solution

    |

  3. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

    Text Solution

    |

  4. if int(1-5sin^2x)/(cos^5xsin^2x)dx=f(x)/(cos^5x)+c then f(x)

    Text Solution

    |

  5. int(x^(7m)+x^(2m)+x^m)(2x^(6m)+7x^m+14)^(1/m)dx

    Text Solution

    |

  6. int (x dx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))) is equal to

    Text Solution

    |

  7. intsqrt(x-3)(sin^(-1)(Inx)+cos^(-1)(Inx))dx is equal to

    Text Solution

    |

  8. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

    Text Solution

    |

  9. inte^(x^(4))(x+x^(3)+2x^(5))e^(x^(2))dx is equal to

    Text Solution

    |

  10. int(sin(101x).sin^(99)x)dx equals

    Text Solution

    |

  11. Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c where C is a...

    Text Solution

    |

  12. int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx is equal to

    Text Solution

    |

  13. If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + ...

    Text Solution

    |

  14. Let f(x) be a quadratic function such that f(0)=1 and int(f(x))/(x^2(x...

    Text Solution

    |

  15. int (x dx)/(sqrt(1+x^(2)+sqrt((1+x^(2))^(3))) is equal to

    Text Solution

    |

  16. int(e^(x)(x-1)(x-lnx))/(x^(2))dx is equal to

    Text Solution

    |

  17. intx^(27)(1+x+x^(2))^(6)(6x^(2)+5x+4)dx=

    Text Solution

    |

  18. Let f (x) be a quadratic function such that f (0) =1 and f(-1)=4, if...

    Text Solution

    |

  19. Evaluate int(e^(tan^(-1)x))/((1+x^(2)))[(sec^(-1)sqrt(1+x^(2)))^(2)+"c...

    Text Solution

    |

  20. int (x^2(xsec^2x+tanx))/(xtanx+1)^2

    Text Solution

    |