Home
Class 12
MATHS
If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-...

If `int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x))` where f(x) is of the form of `ax^(2)+bx+c`, then the value of f(1) is

A

4

B

5

C

6

D

none

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int(2x+3)/((x^(2)+3x)(x^(2)+3x+2)+1)dx`
Put `x^(2)+3x=t" "rArr(2x+3)dx=dt`
`rArr`
`I=int(dt)/(t(t+2)+1),int (dt)/((t+1)^(2))=C-(1)/(t+1)=C-(1)/(x^(2)+3x+1)`
`rArr" "f(1)=5`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE|Exercise JEE Advanced Previous Year|1 Videos

  • HYPERBOLA

    CENGAGE|Exercise JEE Advanced Previous Year|14 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If int ((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-1/(f(x)) where f(x) is of the form of ax^(2)+bx+c then (a+b+c) equals

If f(x)=2x-x^(2) then find the value of f(1)=____.

If int(dx)/(x^(2)+ax+1)=f(g(x))+c, then

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

If int f'(x) e^(x^(2))dx = (x-1)e^(x^(2))+c then f (x) is . . . . .

"If"int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is a constant of integration, then the function f(x) is equal to

IF f(x) = ( x+2)/(3x-1) , then f(f(x)) is

If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0) , and f(0) = 0, then the value of f(1) is

If f(x)=inte^(x)(tan^(-1)x+(2x)/((1+x^(2))^(2)))dx,f(0)=0 then the value of f(1) is

If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c ,t h e n f(x) is an even function f(x) is a bounded function the range of f(x) is (0,1) f(x) has two points of extrema

CENGAGE-INDEFINITE INTEGRATION-Single Correct Answer Type
  1. int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals

    Text Solution

    |

  2. int((2x+1))/((x^(2)+4x+1)^(3//2))dx

    Text Solution

    |

  3. If int((2x+3)dx)/(x(x+1)(x+2)(x+3)+1)=C-(1)/(f(x)) where f(x) is of th...

    Text Solution

    |

  4. The integral intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx equals

    Text Solution

    |

  5. int(dx)/(xsqrt(x^(6)+1)) equals

    Text Solution

    |

  6. int(dx)/((1+sqrtx)^(2010))=2[(1)/(alpha(1+sqrtx)^(alpha))-(1)/(beta(1+...

    Text Solution

    |

  7. int(sin((pi)/(4)-x)dx)/(2+sin2x)=A tan^(-1)(f(x))+B, where A, B are co...

    Text Solution

    |

  8. If sqrt(x+sqrt(x^(2)+x))dx=A{x+sqrt(x^(2)+2)}^(3//2)+(B)/(sqrt(x+sqrt(...

    Text Solution

    |

  9. int(x^(2)+1)/(xsqrt(x^(2)+2x-1)sqrt(1-x^(2)-x))dx is equal to

    Text Solution

    |

  10. int(dx)/(x^(2)sqrt(16-x^(2))) has the value equal to

    Text Solution

    |

  11. If int(3tan(x-(pi)/(4)))/(cos^(2)xsqrt(tan^(3)x)+tan^(2)x+tanx)=Ktan^(...

    Text Solution

    |

  12. int(sqrt(1-x^(2))-x)/(sqrt(1-x^(2))(1+xsqrt(1-x^(2))))dx is

    Text Solution

    |

  13. int(3x^(2)+2x)/(x^(6)+2x^(5)+x^(4)+2x^(3)+2x^(2)+5)dx=

    Text Solution

    |

  14. int(1)/((1+sqrtx)sqrt(x-x^(2)))dx is equal to

    Text Solution

    |

  15. If f(x) = int(5x^(8)+7x^(6))/((x^(2)+1+2x^(7))^(2))dx, (x ge 0), and f...

    Text Solution

    |

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

    Text Solution

    |

  17. If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C, then f(x) is eq...

    Text Solution

    |

  18. int(x^(2)(1-logx))/((logx)^(4)-x^(4))dx equals

    Text Solution

    |

  19. If int(x(x-1))/((x^(2)+1)(x+1)sqrt(x^(3)+x^(2)+x))dx =(1)/(2)log(e)...

    Text Solution

    |

  20. int(dx^(3))/(x^(3)(x^(n)+1)) equals

    Text Solution

    |