Home
Class 12
MATHS
If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ d...

If `int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + c` where `lambda and mu` are rational number in its simplest form then `(lambda+1/mu)` is equal to

A

1

B

2

C

3

D

6

Text Solution

Verified by Experts

The correct Answer is:
c
Let `I=int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx` then ,
`rArrI=inte^(x)((1+(1-x^(2)))/((1-x)sqrt(-x^(2))))dx`
`=inte^(x){(1)/((1-x)sqrt(1-x^(2)))+sqrt((1+x)/(1-x))}dx`
`rArrI=e^(x)sqrt((1+x)/(1-x))+C`
`thereforelambda=(1)/(2)andmu=1`
Hence , 2 `(lambda+mu)=3`.
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRALS

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

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Exercise|62 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 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

If int_(-2)^(lambda)(3x^(2)+2x+4)dx=32 then lambda=

If the integral I=int(dx)/(x^(10)+x)=lambda ln ((x^(9))/(1+x^(mu)))+C , (where, C is the constant of integration) then the value of (1)/(lambda)+mu is equal to

If 5cos 2t + 12sin 2t = lambda sin(2t -tan^(-1)mu) where lambda, mu are constants then lambda =____ and mu = ______.

If x(sgn x)(sgn x)+|x|(sgnx)^(3)=lambda x^(mu), then the value of lambda+mu is:

If I=int(dx)/(x^(3)(x^(8)+1)^(3//4))=(lambda(1+x^(8))^((1)/(4)))/(x^(2))+c (where c is the constant of integration), then the value of lambda is equal to

OBJECTIVE RD SHARMA-INDEFINITE INTEGRALS-Solved Example
  1. The integral int(1+x-1/x)e^(x+1/x)dx is equal to

    Text Solution

    |

  2. int e^(x^4) (x + x^3 +2x^5) e^(x^2) dx is equal to

    Text Solution

    |

  3. int[sin(101 x)*sin^(99)x]dx

    Text Solution

    |

  4. Suppose int(1-7cos^2x)/(sin^7xcos^2x)dx=(g(x))/(sin^7x)+c where C is a...

    Text Solution

    |

  5. int(x^(2)+x)(x^(-8)+2x^(-9))^(1//10)dx is equal to

    Text Solution

    |

  6. If int 2/(2-x)^2 ((2-x)/(2+x))^(1//3)\ dx = lambda ((2+x)/(2-x))^mu + ...

    Text Solution

    |

  7. Let f(x) be a quadratic function such that f(0)=1 and int(f(x))/(x^2(x...

    Text Solution

    |

  8. int(x)/(sqrt(1+x^(2)+sqrt(1+x^(2))^(3)))dx is equal to

    Text Solution

    |

  9. inte^(x)((x-1)(x-logx))/(x^(2))dx is equal to

    Text Solution

    |

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

    Text Solution

    |

  11. Let f (x) be a quadratic function such that f (0) =1 and f(-1)=4, if...

    Text Solution

    |

  12. Evaluate: int(e^tan^((-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)((...

    Text Solution

    |

  13. intx^(2)((xsec^(2)x+tanx))/((xtanx+1)^(2))dx=

    Text Solution

    |

  14. int (mx^(m+2n-1)-nx^(n-1))/(x^(2m+2n)+2x^(m+n)+1)dx is equal to

    Text Solution

    |

  15. int(1)/(tanx+cotx+secx+"cosec "x)dx is equal to

    Text Solution

    |

  16. int(x^(2)(1-"In "x))/(("In "x)^(4)-x^(4))dx is equal to

    Text Solution

    |

  17. The integral int(2x^(12)+5x^(9))/((x^(5)+x^(3)+1)^(3))dx is equal to ...

    Text Solution

    |

  18. If int(1)/(cos^(3)xsqrt(2 sin2x))dx=(tanx)^(A)+C(tanx)^(B)+k, where k...

    Text Solution

    |

  19. "If"int(dx)/(x^(3)(1+x^(6))^(2/3))=f(x)(1+x^(6))^(1/3)+C where, C is a...

    Text Solution

    |

  20. The integral int(1)/((1+sqrt(x))sqrt(x-x^(2)))dx is equal to (where C ...

    Text Solution

    |