Home
Class 12
MATHS
Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3t...

`Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n` both `f(x)a n dg(x)` are odd functions `f(x)` is monotonic function `f(x)=g(x)` has no real roots `int(f(x))/(g(x))dx=-1/x+3/(x^3)+c`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

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

If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric function for |a|>2 f(x) is logarithmic function for |a| 2 g(x) is rational function for |a|<2

int(x+1)/(x(1+x e^x)^2)dx=log|1-f(x)|+f(x)+c , then f(x)=

Let f(x)=tanxa n dg(f(x))=f(x-pi/4), where f(x)a n dg(x) are real valued functions. Prove that f(g(x))="tan ((x-1)/(x+1))dot

If f(x)a n dg(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that d/(dx)[f(x)g(x)]=f(x)d/(dx){g(x)}+g(x)d/(dx){f(x)}

If f(x) and g(x) are two real functions such that f(x)+g(x)=e^(x) and f(x)-g(x)=e^(-x) , then

Let f(x) = tan^-1 (g(x)) , where g (x) is monotonically increasing for 0 < x < pi/2.

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

If function f(x)=x^(2)+e^(x//2) " and " g(x)=f^(-1)(x) , then the value of g'(1) is

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

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Each question has four choices, a,b,c and d, out of which only one i...

    Text Solution

    |

  2. If int(x^2-x+1)/((x^2+1)^(3/2))e^x dx=e^xf(x)+c, then (a) f(x) is an ...

    Text Solution

    |

  3. Ifint(x^4+1)/(x^6+1)dx=tan^(-1)f(x)-2/3tan^(-1)g(x)+C ,t h e n both f...

    Text Solution

    |

  4. If intsin^(-1)xcos^(-1)xdx=f^(-1)(x) [π/2x-xf^(-1)(x)-2sqrt(1-x^2)]+2...

    Text Solution

    |

  5. If int(cos4x+1)/(cotx-tanx)dx = Acos4x+B ,t h e n (a)A=-1/8 (b) B=1/...

    Text Solution

    |

  6. Statement 1: int(dx)/(x^3sqrt(1+x^4))=-1/2sqrt(1+1/(x^4))+C Statement...

    Text Solution

    |

  7. Statement 1: int(sinxdx)/x ,(x >0), cannot be evaluated. Statement 2:...

    Text Solution

    |

  8. int(4e^x+6e^(-x))/(9e^x-4e^(-x))dx=A x+Blog(9e^(2x)-4)+C ,t h e n A= ...

    Text Solution

    |

  9. The value of the integral int(cos^3x+cos^5x)/(sin^2x+sin^4x)dxi s si...

    Text Solution

    |

  10. Evaluate: intsin^(-1)((2x+2)/(sqrt(4x^2+8x+13)))dx

    Text Solution

    |

  11. Evaluate: for m in N , intx^(3m)+x^(2n)+x^m)(2x^(2m)+3x^m+6)^(1/m)dx...

    Text Solution

    |

  12. Evaluate: int(cos^4x)/(sin^3x(sin^5x+cos^5x)^(3/5))dx

    Text Solution

    |

  13. Evaluate: int sqrt(1+cosec x) dx ,(0 < x < pi/2)

    Text Solution

    |

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

    Text Solution

    |

  15. The integral int(sec^2x)/((secx+tanx)^(9/2))dx equals (for some arbitr...

    Text Solution

    |

  16. Evaluate: int(dx)/(x^3sqrt(x^2-1))

    Text Solution

    |

  17. Evaluate : int(2x)/((1-x^2)sqrt(x^4-1))dx

    Text Solution

    |

  18. Evaluate: intsqrt(secx-1)dx

    Text Solution

    |

  19. Evaluate: intsqrt((3-x)/(3+x))sin^(-1)(1/6sqrt(3-x))dx

    Text Solution

    |

  20. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

    Text Solution

    |