Home
Class 12
MATHS
The value of the integral int(log(x+1)-...

The value of the integral `int(log(x+1)-logx)/(x(x+1))dx` is

A

`(1)/(2)[log(x+1)]^(2)+(1)/(2)(logx)^(2)+log(x+1)logx+C`

B

`-(1)/(2)[{log(x+1)}^(2)+(logx)^(2)]+log(x+1).logx+C`

C

`(1)/(2)[log(1+1//x)]^(2)+C`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
b
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • INDEFINITE INTEGRALS

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

The value of the integral int_(-1)^(1)log(x+sqrt(x^(2)+1))dx is

The value of integral int_(1)^(0)(log(1+x))/(1+x^(2))dx , is

The value of the integral int_(0)^(pi)x log sin x dx is

Evaluate the following integrals: int(log(logx))/(x)dx

∫(log(x + 1) - logx)/{x(x + 1)} dx is equal to

The value of integral int_(1)^(e) (log x)^(3)dx , is

int(log(logx))/(x.logx)dx=

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

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Exercise
  1. If int(dx)/(5-4cosx)=Atan^(-1)(Btanx//2)+C, then

    Text Solution

    |

  2. If I=int(dx)/(x^(4)sqrt(a^(2)+x^(2))), then I equals

    Text Solution

    |

  3. The value of the integral int(log(x+1)-logx)/(x(x+1))dx is

    Text Solution

    |

  4. But for all arbitrary constants, intsqrt((1+sintheta-sin^(2)theta-s...

    Text Solution

    |

  5. If x^2!=n pi-1, n in N. Then, the value of int x sqrt((2sin(x^2+1)-sin...

    Text Solution

    |

  6. Given f(x) =|{:(0,x^(2)-sinx,cosx-2),(sinx-x^(2),0,1-2x),(2-cosx,2x-1,...

    Text Solution

    |

  7. int(1)/(x^(1//2)(1+x^(2))^(5//4))dx is equal to

    Text Solution

    |

  8. int(x^(2))/((a+bx^(2))^(5//2))dx is equal to

    Text Solution

    |

  9. int(sin^(3)x)/((1+cos^(2)x)sqrt(1+cos^(2)x+cos^(2)x+cos^(4))x)dx is eq...

    Text Solution

    |

  10. int(1)/(sqrt(sin^(3)xsin(x+alpha)))dx is equal to

    Text Solution

    |

  11. The antiderivative of (3^(x))/(sqrt(1-9^(x))) with respect to x is

    Text Solution

    |

  12. Integration of (1)/(sqrt(x^(2)=9)) with respect to (x^(2)+1) is equa...

    Text Solution

    |

  13. If int(sintheta-costheta)/((sintheta+costheta)sqrt(sinthetacostheta+s...

    Text Solution

    |

  14. The primitive of the function f (x) =(2x+1)|cosx|, when (pi)/(2)ltxl...

    Text Solution

    |

  15. The primitive of the function f (x) = (2x+1) |sinx|, where piltxlt2p...

    Text Solution

    |

  16. Let intsqrt((5-x)/(2+x))dx equal

    Text Solution

    |

  17. The value of the integral int(xsin x^(2)e^(secx^(2)))/(cos^(2)x^(2))dx...

    Text Solution

    |

  18. int(x^(2)-1)/(xsqrt((x^(2)+alphax+1))(x^(2)+betax+1))dx is equal to

    Text Solution

    |

  19. Evaluate: int(e^(2x)-2e^x)/(e^(2x)+1)dx

    Text Solution

    |

  20. int(1)/(cosx-sinx)dx is equal to

    Text Solution

    |