Home
Class 12
MATHS
The value of the integral int0^(log5)(e^...

The value of the integral `int_0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx`

A

`3+2pi`

B

`4-pi`

C

`2+pi`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Putting `e^(x)-1=t^(2)` in the given integral, we have
`int_(0)^(log5) (e^(x)sqrt(e^(x)-1))/(e^(x)+3) dx=2 int_(0)^(2) (t^(2))/(t^(2)+4) dt =2 (int_(0)^(2) 1 dt -4int_(0)^(2) (dt)/(t^(2)+4))`
`=2[(t-2 tan^(-1)(t/2))_(0)^(2)]`
`=2[(2-2xxpi//4)]=4-pi`
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise MCQ_TYPE|27 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise LC_TYPE|31 Videos

  • DEFINITE INTEGRATION

    CENGAGE PUBLICATION|Exercise CAE_TYPE|88 Videos

  • CURVE TRACING

    CENGAGE PUBLICATION|Exercise EXERCISES|24 Videos

  • DETERMINANT

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer|5 Videos

Similar Questions

Explore conceptually related problems

The value of the integral int_0^1e^(x^2)dx

Evaluate : int_0^log5(e^x(e^x-1)^(1/2))/(e^x+3)dx

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

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

The value of the integral int_(-1)^(+1){(x^(2013))/(e^(|x|)(x^(2)+cosx))+(1)/(e^(|x|))}dx

The value of the integral int_(-1)^(1){(x^(2015))/(e^(|x|)(x^(2) + cos x)) + (1)/(e^(|x|))} dx is equal to

The value of the integral int_(-1)^(+1){(x^(2013))/(e^(|x|)(x^(2)+cos x))+(1)/(e^(|x|))}dx is equal to

The value of the integral int_(e^(-1))^(e^2)|((log)_e x)/x| dx is (A) 3/2 (B) 5/2 (C) 3 (D) 5

int (e^(x))/(1+e^(x))dx

The value of the definite integral int_(0)^(1)(1+e^(-x^(2))) dx is

CENGAGE PUBLICATION-DEFINITE INTEGRATION -SCQ_TYPE
  1. int(5/2)^5(sqrt((25-x^2)^3))/(x^4)dx is equal to

    Text Solution

    |

  2. If f(x) satisfies the condition of Rolle's theorem in [1,2], then int1...

    Text Solution

    |

  3. The value of the integral int0^(log5)(e^xsqrt(e^x-1))/(e^x+3)dx

    Text Solution

    |

  4. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

    Text Solution

    |

  5. int0^oo(dx)/([x+sqrt(x^2+1)]^3)is equal to (a)3/8 (b) 1/8 (c) -3/8 ...

    Text Solution

    |

  6. If f(y)=e^y ,g(y) = y>0,a n d \ F(t)=int0^t f(t-y)g(y)dy ,then

    Text Solution

    |

  7. about to only mathematics

    Text Solution

    |

  8. The numbers of possible continuous f(x) defined in [0,1] for which I1...

    Text Solution

    |

  9. Suppose that F(x) is an anti-derivative of f(x)=(sinx)/x ,w h e r ex >...

    Text Solution

    |

  10. int(-pi/3)^0[cot^(-1)(2/(2cosx-1))+cot^(-1)(cosx-1/2)]dxi se q u a lto...

    Text Solution

    |

  11. Evaluate the definite integrals int(0)^(pi//4)(sinx+cosx)/(25-16(...

    Text Solution

    |

  12. int- 1^1(e^(-1/ x))/(x^2(1+e^(-2/ x)))dx is equal to :

    Text Solution

    |

  13. If int0^oosinx/xdx=pi/2, then int0^oosin^3x/xdx is equal to

    Text Solution

    |

  14. The range of the function f(x)=int(-1)^(1)(sinxdt)/(1-2tcosx+t^(2)) is

    Text Solution

    |

  15. If the function f : [0,8] to R is differentiable, then for 0 < alpha...

    Text Solution

    |

  16. If f(x)=x^(5)+5x-1 then int(5)^(41)(dx)/((f^(-1)(x))^(5)+5f^(-1)(x)) e...

    Text Solution

    |

  17. Let f(0)=0a n dint0^2f^(prime)(2t)e^(f(2t))dt=5.t h e nv a l u eoff(4)...

    Text Solution

    |

  18. If f(x)="cos"(tan^(-1)x), then the value of the integral int0^1xf''(x)...

    Text Solution

    |

  19. The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)...

    Text Solution

    |

  20. The value of int1^e((tan^(-1)x)/x+(logx)/(1+x^2))dx ,is (a) tane (b)...

    Text Solution

    |