Home
Class 12
MATHS
int(x^(x))^(x)(2x log(e)x+x)dx is equal ...

`int(x^(x))^(x)(2x log_(e)x+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 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

intx^(x)(1+log_(e)x) dx is equal to

int_(1)^(3)|(2-x)log_(e )x|dx is equal to:

int cos (log_e x)dx is equal to

int (f'(x))/( f(x) log(f(x)))dx is equal to

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

int{sin(log_(e)x)+cos(log_(e)x)}dx is equal to

int(1)/(x cos^(2)(log_(e)x))dx

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

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

int x ^(x)((ln x )^(2) +lnx+1/x) dx is equal to:

OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
  1. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

    Text Solution

    |

  2. int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x...

    Text Solution

    |

  3. int(x^(x))^(x)(2x log(e)x+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. Evaluate the following Integrals : int (sec x .dx)/(sqrt(sin (x+2A...

    Text Solution

    |

  7. "Let "int e^(x){f(x)-f'(x)}dx=phi(x). " Then "int e^(x) f(x)dx " is "

    Text Solution

    |

  8. Evaluate "if " int(1)/(x+x^(5))dx=f(x)+c," then " int(x^(4))/(x+x^(5...

    Text Solution

    |

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

    Text Solution

    |

  10. If n is an odd positive integer, then int|x^(n)|dx is equal to

    Text Solution

    |

  11. If inte^(ax)cosbx dx=(e^(2x))/(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 (dx)/(1- sin ^(4)x )= a tan x +b tan ^(-1) (c tan x )+ D, 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)dx)/((1+x^(2))(1+sqrt(1+x^(2))))and f(0)=0. f(x) i...

    Text Solution

    |