Home
Class 12
MATHS
If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1...

If `int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C` , then `k` is equal to `-1/((log)_e2)` (b) `(log)_e2` (c) `-1` (d) `1/2`

Text Solution

Verified by Experts

`I=∫(2^(1/x))/(x^2)​​dx=k.2^(1/x)​+C .......(1)`
Let `1/x​=t`
`⇒(dx)/(x^2)​=−dt`
`I=−∫2^t.dt`
...
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

  • INVERSE TRIGONOMETRIC FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|523 Videos

Similar Questions

Explore conceptually related problems

int(e^(ln tan^(-1)x))/(1+x^(2))dx

If int (x^4 + 1)/(x(x^2+1)^2)\ dx = A ln |x| +B/(1+x^2)+C, then A+B equals to :

If int_(log" "2)^(x)(du)/((e^(u)-1)^(1//2))=(pi)/(6) , then e^(x) is equal to

int _(-1//2)^(1//2) cos x log ((1+x)/(1-x)) dx = k log 2 , then k equals

int_(e^(-1))^(e^(2))|(ln x)/(x)|dx

If int(2)/(1-x^(4))dx = k log[(1+x)/(1-x)]+tan^(-1)x + c then k=

" (2) "int_(1)^(2)(log e^(x))/(x^(2))dx

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int_(2)^(e)((1)/(ln x)-(1)/(ln^(2)x))dx

int_(pi//6)^(pi//3)1/(sin2x)dx\ is equal to (log)_e3 b. (log)_"e"sqrt(3) c. 1/2log(-1) d. log(-1)

RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. If int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=asin2x+C , then a= -1//2 (b...

    Text Solution

    |

  2. int(x-1)\ e^(-x)\ dx is equal to x e^x+C (b) x e^x+C (c) -x e^(-x)+C ...

    Text Solution

    |

  3. If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal...

    Text Solution

    |

  4. int1/(1+tanx)\ dx=

    Text Solution

    |

  5. int|x|^3\ dx is equal to ( x^4)/4+C (b) (|x|^4)/4+C (c) (x^4)/4+C (d) ...

    Text Solution

    |

  6. Evaluate: int(cossqrt(x))/(sqrt(x))\ dx

    Text Solution

    |

  7. inte^x(1-cotx+cot^2x)dx= e^xcotx+C (b) e^xcotx+C (c) e^x\ cos e c\ ...

    Text Solution

    |

  8. int(sin^6x)/(cos^8x)\ dx= tan7x+C (b) (tan^7x)/7+C (c) (tan7x)/7+C (d...

    Text Solution

    |

  9. int1/(7+5cosx)\ dx= 1/(sqrt(6))tan^(-1)(1/(sqrt(6))tanx/2)+C (b) 1/(s...

    Text Solution

    |

  10. int1/(1+cosx+sinx)\ dx= log|1+cotx/2|+C (b) log|1-tanx/2|+C (c) log|...

    Text Solution

    |

  11. int(x+3)/((x+4)^2)e^x\ dx= (e^x)/(x+4)+C (b) (e^x)/(x+3)+C (c) 1/((x+...

    Text Solution

    |

  12. int(sinx)/(3+4cos^2x)\ dx log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((...

    Text Solution

    |

  13. int e^x ((1-sinx)/(1-cosx)) dx= (A) e^xtan(x/2)+C (B) e^xcot(x/...

    Text Solution

    |

  14. int2/((e^x+e^(-x))^2)\ dx ( e^(-x))/(e^x+e^(-x))+C (b) -1/(e^x+e^(-x)...

    Text Solution

    |

  15. int(e^x(1+x))/(cos^2(x e^x))\ dx= 2(log)ecos(x e^x)+C (b) sec(x e^x)+...

    Text Solution

    |

  16. int(sin^2x)/(cos^4x)\ dx= 1/3tan^2x+C (b) 1/2tan^2x+C (c) 1/3tan^3x+C...

    Text Solution

    |

  17. The primitive of the function f(x)=(1-1/(x^2))a^(x+1/x)\ ,\ a >0 is...

    Text Solution

    |

  18. The value of int1/(x+xlogx)\ dx is 1+logx (b) x+logx (c) xlog(1+logx)...

    Text Solution

    |

  19. intsqrt(x/(1-x))\ dx is equal to sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x...

    Text Solution

    |

  20. Evaluate: inte^x(f(x)+f^(prime)(x))dx=e^xf(x)+C

    Text Solution

    |