Home
Class 12
MATHS
int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x...

`int \ {f(x)*g^(prime)(x)-f^(prime)(x)g(x))/(f(x)*g(x)){logg(x)-logf(x)} \ dx`

A

`log_(e){(g(x))/(f(x))}+C`

B

`(1)/(2){"log"_(e)(g(x))/(f(x))}^(2)+C`

C

`(g(x))/(f(x))"log"_(e)(g(x))/(f(x))+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Let `I=int(f(x)g'(x)-g(x)f'(x))/(f(x)*g(x)){log(x)-logf(x)}dx`
`rArrI=intlog{(g(x))/(f(x))}*d{"log"(g(x))/(f(x))}=(1)/(2){"log"_(e)(g(x))/(f(x))}^(2)+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(f(x)*g'(x)-f'(x)g(x))/(f(x)*g(x)){log g(x)-log f(x)}dx

int(f(x)*g\'(x)-f\'(x)g(x))/(f(x)*g(x))*{logg(x)-logf(x)}dx= (A) log (g(x)/f(x))+c (B) log (f(x)/g(x))+c (C) 1/2log (g(x)/f(x))^2+c (D) none of these

int_( is )((f(x)g'(x)-f'(x)g(x))/(f(x)g(x)))*(log(g(x))-log(f(x))dx

If int(f^(prime)(x)g(x)-g^(prime)(x)f(x))/((f(x)+g(x))sqrt(f(x)g(x)-g^2(x)))d x=sqrt(m)tan^(- 1)(sqrt((f(x)-g(x))/(ng(x))+C) where m,n in N and 'C' is constant of integration (g(x) > 0). Find the value

int(f(x)g'(x)+g(x)f'(x))/(f(x)g(x))[logf(x)+logg(x)]dx=

Evaluate int[f(x)g^(n)(x)-f^(n)(x)g(x)]dx

int[f(x).phi'(x)-f'(x).phi(x)]/[f(x).phi(x)]{logphi(x)-logf(x)}.dx is equal to

int(f'(x))/(f(x).logf(x))dx=

int x{f(x^(2))g'(x^(2))-f'(x^(2))g(x^(2))}dx

Suppose fa n dg are functions having second derivative f'' and g' ' everywhere. If f(x)dotg(x)=1 for all xa n df^(prime)a n dg' are never zero, then (f^('')(x))/(f^(prime)(x))-(g^('')(x))/(g^(prime)(x))e q u a l (a)(-2f^(prime)(x))/f (b) (2g^(prime)(x))/(g(x)) (c)(-f^(prime)(x))/(f(x)) (d) (2f^(prime)(x))/(f(x))

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
  1. int(tanx)/(sqrt(sin^(4)x+cos^(4)x))dx is equal to

    Text Solution

    |

  2. If int \ sqrt(cos^3x/sin^11x) \ dx = -2(A tan^(9//2)x + B tan^(5//2) x...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. intsin2xlog(e)cosx dx is equal to

    Text Solution

    |

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

    Text Solution

    |