Home
Class 12
MATHS
intsqrt(e^x-1)dx is equal to (a) 2[sqr...

`intsqrt(e^x-1)dx` is equal to
(a) `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c`
(b) `sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)+c`
(c) `sqrt(e^x-1)+tan^(-1)sqrt(e^x-1)+c`
(d) `2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+c`

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s 1/2((sqrt(x^2-1))/(x^3)+tan^(-1)sqrt(x^2-1))+C , 1/2((sqrt(x^2-1))/(x^2)+xtan^(-1)sqrt(x^2-1))+C , 1/2((sqrt(x^2-1))/x+tan^(-1)sqrt(x^2-1))+C , 1/2((sqrt(x^2-1))/(x^2)+tan^(-1)sqrt(x^2-1))+C

int (dx)/(sqrt(2e^(x)-1))=2 sec^(-1)(sqrt(2)e^((x)/(2)))+c

int(sqrt(x-1))/(xsqrt(x+1))dx is e q u a l to ln|x-sqrt(x^2-1)|-tan^(-1)x+c, ln|x+sqrt(x^2-1)|-tan^(-1)x+c , ln|x-sqrt(x^2-1)|-sec^(-1)x+c, ln|x+sqrt(x^2-1)|-sec^(-1)x+c

If y=e^(sqrt(x))+e^(-sqrt(x)) , then (dy)/(dx) is equal to (a) (e^(sqrt(x)))/(2sqrt(x)) (b) (e^(sqrt(x))-e^(-sqrt(x)))/(2sqrtx) (c) 1/(2sqrt(x))sqrt(y^2-4) (d) 1/(2sqrt(x))sqrt(y^2+4)

Prove that ( tan^(-1) 1/e)^2 + (2e) / sqrt(e^2+1) <(tan^(-1)e)^2+2/(sqrt(e^2+1))

d/(dx)(cos^(-1)sqrt(cosx)) is equal to (a) 1/2sqrt(1+s e cx) (b) sqrt(1+secx) (c) -1/2sqrt(1+secx) (d) -sqrt(1+secx)

tan^(-1)x+tan^(-1) (1-x) = 2 tan ^(-1) sqrt(x(1-x))

d/(dx)[tan^(-1)((sqrt(x)(3-x))/(1-3x))] is (a) 1/(2(1+x)sqrt(x)) (b) 3/((1+x)sqrt(x)) (c) 2/((1+x)sqrt(x)) (d) 3/(2(1+x)sqrt(x))

Solve: tan^(-1)sqrt(x(x+1) + sin^(-1)sqrt(1+x+x^2) = pi/2

Differentiate tan ^(-1)((sqrt(1+x^2 )-1)/x) w,r,t. tan ^(-1)x

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= (a) sqrt(x^2+1/(x^2)+1)+C (b) (...

    Text Solution

    |

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

    Text Solution

    |

  3. intsqrt(e^x-1)dx is equal to (a) 2[sqrt(e^x-1)-tan^(-1)sqrt(e^x-1)]+...

    Text Solution

    |

  4. If intsinx d(secx)=f(x)-g(x)+c ,t h e n f(x)=secx (b) f(x)=tanx g(x...

    Text Solution

    |

  5. If I=int(sinx+sin^3x)/(cos2x)dx=Pcosx+Qlog|f(x)|+R , then (a)P=1/2,Q...

    Text Solution

    |

  6. If int(e^(x-1))/((x^2-5x+4))2xdx=A F(x-1)+B F(x-4)+C and F(x)=int(e^x)...

    Text Solution

    |

  7. Evaluate: int1/xsqrt((1-sqrt(x))/(1+sqrt(x))dx)

    Text Solution

    |

  8. int (x^3 + 3x + 2)/((x^2 + 1)^2 (x + 1)) dx

    Text Solution

    |

  9. int(3+2cosx)/((2+3cosx)^2)dx is equal to (a) ((sinx)/(3cosx+2))+c ...

    Text Solution

    |

  10. int((x+2)/(x+4))^2 e^xdx is equal to

    Text Solution

    |

  11. IfI=int(sin2x)/((3+4cosx)^3)dx ,t h e nIe q u a l s (a)(3cosx+8)/((...

    Text Solution

    |

  12. If I=int (dx)/(secx + cosec x), then equals

    Text Solution

    |

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

    Text Solution

    |

  14. inte^(tanx)(secx-sinx)dx"is equal to"

    Text Solution

    |

  15. int e^x((x^2+1))/((x+1)^2)dx is equal to (a) ((x-1)/(x+1))e^x+c (b)...

    Text Solution

    |

  16. intxsinxsec^3xdx" is equal to

    Text Solution

    |

  17. IfI=int(dx)/(x^3sqrt(x^2-1)),t h e nIe q u a l s 1/2((sqrt(x^2-1))/(...

    Text Solution

    |

  18. int(ln((x-1)/(x+1)))/(x^2-1)dx is equal to (a)1/2(ln((x-1)/(x+1)...

    Text Solution

    |

  19. Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(...

    Text Solution

    |

  20. "Let " k(x)=int((x^(2)+1)dx)/(root(3)(x^(3)+3x+6)) " and " k(-1)=(1)/(...

    Text Solution

    |