Home
Class 12
MATHS
int(x^x)^x(2xlogex+x)dx is equal to...

`int(x^x)^x(2xlog_ex+x)dx` is equal to

A

`x(x^(x))+C`

B

`(x^(x))+C`

C

`x^(x).log_(e)x+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Let `I=int(x^(x))(2xlog_(e)x+x)dx=intx^(x^(2))(2xlog_(e)x+x)dx`
`rArrI=int1.d(x^(x^(2)))=x^(x^(2))+C=(x^(x))^(x)+C`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

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

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|62 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

  • INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Illustration|1 Videos

Similar Questions

Explore conceptually related problems

int(xlog_ex)dx

int(1)/(x)(log_(ex)e)dx is equal to

int x^(2)dx is equal to:

int (x+3)/(x+4)^2e^x dx is equal to

int((x+2)/(x+4))^(2)e^(x)dx is equal to

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

int(2x^(3)-1)/(x^(4)+x)dx is equal to

inte^(x)((x-1))/(x^(2))dx is equal to

inte^(x)((x-1)(x-logx))/(x^(2))dx is equal to

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
  1. int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)...

    Text Solution

    |

  2. int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)...

    Text Solution

    |

  3. int(x^x)^x(2xlogex+x)dx is equal to

    Text Solution

    |

  4. Let the equation of a curve passing through the point (0,1) be given b...

    Text Solution

    |

  5. Evaluate: int1/(sin^4x+cos^4x)dx

    Text Solution

    |

  6. int secx/(sqrt(sin(2x+alpha)+sinalpha))dx

    Text Solution

    |

  7. Let inte^(x){f(x)-f'(x)}dx=phi(x). then, inte^(x)f(x)dx is equal to

    Text Solution

    |

  8. If int1/(x+x^5)dx=f(x)+c ,then evaluate int(x^4)/(x+x^5)dxdot

    Text Solution

    |

  9. If int f(x)dx=F(x), then intx^3f(x^2)dx is equal to :

    Text Solution

    |

  10. If n is a positive odd integer, then int |x^n| dx=

    Text Solution

    |

  11. If inte^(ax)cosbx dx=(e2x)/(29)f(x)+C , then f'' (x)=

    Text Solution

    |

  12. int(sin^(4)x)/(sin^(4)x+cos^(4)x)dx is equal to

    Text Solution

    |

  13. If intf(x)dx=2 {f(x)}^(3)+C , then f (x) is

    Text Solution

    |

  14. Let g (x) be a differentiable function satisfying (d)/(dx){g(x)}=g(x)...

    Text Solution

    |

  15. If intg(x)dx=g(x), then the value of the integral intf(x)g(x){f(x)+2...

    Text Solution

    |

  16. If int(1)/(1-sin ^(4)x)dx=(1)/(2) tanx+Atan^(-1){f(x)}+C, then

    Text Solution

    |

  17. intsin2xlog(e)cosx dx is equal to

    Text Solution

    |

  18. Let f(x) be a polynomial of degree three f(0) = -1 and f(1) = 0. Also,...

    Text Solution

    |

  19. int(1)/(x(1+root(3)(x))^(2))dxis equal to

    Text Solution

    |

  20. Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

    Text Solution

    |