Home
Class 12
MATHS
int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(...

`int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log_(e)(f(x))+g(x)+C` where C is the constant of integration and f(x) is positive. Then `f(x)+g(x)` has the value equal to

A

`e^(x)+sinx+2x`

B

`e^(x)+sinx`

C

`e^(x)-sinx`

D

`e^(x)+sinx+x`

Text Solution

Verified by Experts

The correct Answer is:
B
`I=int((e^(x)+cosx+1)-(e^(x)+sinx+x))/(e^(x)+sinx+x)`
`=log_(e)(e^(x)+sinx+x)-x+C`
`therefore" "f(x)=e^(x)+sin x+x and g(x)=-x`
`" "f(x)+g(x)=e^(x)+sinx`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Subjective Type|6 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • INDEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise Archives JEE ADVANCED (Single Correct Answer Type)|1 Videos

  • HYPERBOLA

    CENGAGE PUBLICATION|Exercise COMPREHENSION TYPE|2 Videos

  • INEQUALITIES AND MODULUS

    CENGAGE PUBLICATION|Exercise Single correct Answer|21 Videos

Similar Questions

Explore conceptually related problems

If inte^(sinx)[(xcos^3x-sinx)/(cos^2x)]dx=e^(sinx)*f(x)+c , where c is constant of integration, then f(x)=

If int (x+1)/(sqrt(2x-1))dx = f(x)sqrt(2x-1)+C , where C is a constant of integration, then f(x) is equal to

If int (e^(x)(1+sinx))/(1+cos x)dx=e^(x)f(x)+c , then the value of f(x) is -

If f(x)=log_(x)(log_(e)x) , then the value of f'(e ) is -

If f(x)=log_(5)log_(3)x , then f'(e ) is equal to

If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

If (d)/(dx)f(x)=g(x) , then the value of int_(a)^(b)f(x)g(x)dx is -

If f(x) = log_e ((1-x)/(1+x)) , then f' (0) is

If f(x)=x/(sinx) and g(x)=x/("tan"x) , where 0ltxle1 , then in this interval

CENGAGE PUBLICATION-INDEFINITE INTEGRATION-Single Correct Answer Type
  1. If int(x+(cos^(-1)3x)^(2))/(sqrt(1-9x^(2)))dx=Asqrt(1-9x^(2))+B(cos^(-...

    Text Solution

    |

  2. If int(tan^(9)x)dx=f(x)+log|cosx|, where f(x) is a polynomial of degre...

    Text Solution

    |

  3. int(cosx-sinx+1-x)/(e^(x)+sinx+x)dx=log(e)(f(x))+g(x)+C where C is the...

    Text Solution

    |

  4. Evaluate:int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3)))dx equals

    Text Solution

    |

  5. int(e^(x)(x-2))/(x(x^(2)+e^(x)))dx AAx gt0 is equal to

    Text Solution

    |

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

    Text Solution

    |

  7. The value of int("cosec x")/(cos^(2)(1+logtan.(x)/(2)))dx is

    Text Solution

    |

  8. Evaluate: int(dx)/(xsqrt(x^(6)-16))=

    Text Solution

    |

  9. int (dx)/(cos (2 x)cos (4x)) is equal to

    Text Solution

    |

  10. intx2^(ln(x^(2)+1))dx is equal to

    Text Solution

    |

  11. If int(sinx)/(sin(x-(pi)/(4)))dx=Af(x)+(1)/(sqrt2)log[|sinx-cosx|]+c, ...

    Text Solution

    |

  12. Evaluate: int(sqrt((cosx)/(x))-sqrt((x)/(cosx))sinx)dx equals

    Text Solution

    |

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

    Text Solution

    |

  14. 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

    |

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

    Text Solution

    |

  16. Evaluate :int(dx)/(xsqrt(x^(6)+1)) equals

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |