Home
Class 12
MATHS
Evaluate: (i) int(sin^2x)/(1+cosx)\ dx...

Evaluate:
(i) `int(sin^2x)/(1+cosx)\ dx`
(ii) `int(sec^2x+cos e c^2x)\ dx`

Text Solution

Verified by Experts

(i) `int(sin^2x)/(1+cosx)\ dx`

`=int(1-cos^2x)/(1+cosx)\ dx`

`=int(1-cosx)\dx`

`=x-sinx+C`

(ii) `int(sec^2x+cos e c^2x)\ dx`

`=tanx-cotx+C`
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

Evaluate : int (sin^2x)/(1+cosx) dx.

Evaluate: (i) int(sin4x)/(sin2x)dx( ii) int(sin4x)/(cos2x)dx

(i) int (sin x)/(1+ cos x) dx. (ii) int (sin x)/(1+ cos x)^2 dx.

Evaluate: (i) int(sinx)/(1+cos^2x)\ dx (ii) int(2x^3)/(4+x^8)\ dx

Evaluate : (i) int(sin4x)/(cos2x)dx (ii) int(sin4x)/(sinx)dx

Evaluate: (i) int(2)/(1+cos2x)dx (ii) int(2)/(1-cos2x)dx

Evaluate: (i) int(sin2x)/((a+b cos2x)^(2))dx (ii) int(log x^(2))/(x)dx

Evaluate: (i) int(1-sin x)/(x+cos x)dx (ii) int(a)/(b+ce^(x))dx

Evaluate: (i) int(1)/(sin^(3)x cos^(5)x)dx (ii) int(1)/(sin^(3)x cos x)dx

Evaluate: (i) int(1)/(1-cos x)dx( ii) int(1)/(1-sin x)dx

RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: (i) intsqrt(x)(3-5x)\ dx (ii) int((x+1)(x-2))/(sqrt(x))\ d...

    Text Solution

    |

  2. Evaluate: (i) int(x^5+x^(-2)+2)/(x^2)\ dx (ii) int(5\ x^4+12\ x^3+7...

    Text Solution

    |

  3. Evaluate: (i) int(sin^2x)/(1+cosx)\ dx (ii) int(sec^2x+cos e c^2x)\...

    Text Solution

    |

  4. Evaluate: (i) int(sin^3x-cos^3x)/(sin^2xcos^2x)\ dx (ii) int(5cos^3...

    Text Solution

    |

  5. Evaluate: (i) int(tanx+cotx)^2\ dx (ii) int(1-cos2x)/(1+cos2x)\ dx

    Text Solution

    |

  6. Evaluate: (i) int(cosx)/(1-cosx)\ dx (ii) int(cos^2x-sin^2x)/(sqrt...

    Text Solution

    |

  7. Evaluate: (i) int1/(1-cosx)\ dx (ii) int1/(1-sinx)\ dx

    Text Solution

    |

  8. Evaluate: (i) int(tanx)/(secx+tanx)\ dx (ii) int(cos e c\ x)/(cos e c\...

    Text Solution

    |

  9. Evaluate: (i) int1/(1+cos2x)\ dx (ii) int1/(1-cos2x)\ dx

    Text Solution

    |

  10. Evaluate: (i) inttan^(-1)((sin2x)/(1+cos2x))\ dx (ii) intcos^(-1)(si...

    Text Solution

    |

  11. Evaluate: (i) intcot^(-1)((sin2x)/(1-cos2x))\ dx (ii) intsin^(-1)((2...

    Text Solution

    |

  12. Evaluate: (i) int((x^3+8)(x-1))/(x^2-2x+4)\ dx (ii) int(atanx+bcotx)...

    Text Solution

    |

  13. Evaluate: (i) int(x^3-3x^2+5x-7+x^2\ a^x)/(2x^2)\ dx (ii) int(cosx)...

    Text Solution

    |

  14. Evaluate: (i) int(1-cosx)/(1+cosx)\ dx (ii) int{3sinx-4cosx+5/(cos^...

    Text Solution

    |

  15. If f^(prime)(x)=x-1/(x^2) and f(1)=1/2 , find f(x) .

    Text Solution

    |

  16. If f^(prime)(x)=x+b ,\ \ f(1)=5,\ \ f(2)=13 , find f(x) .

    Text Solution

    |

  17. If f^(prime)(x)=8\ x^3-2x ,\ \ f(2)=8, find f(x) .

    Text Solution

    |

  18. If f^(prime)(x)=asinx+bcosx and f^(prime)(0)=4,\ \ f(0)=3,\ \ f(pi/2)=...

    Text Solution

    |

  19. Write the primitive or anti-derivative of f(x)=sqrt(x)+1/(sqrt(x)) ...

    Text Solution

    |

  20. Evaluate: int{(2x-3)^5+1/((7x-5)^3)+1/(sqrt(5x-4))+1/(2-3x)+sqrt(3x+2)...

    Text Solution

    |