Home
Class 12
MATHS
Evaluate: (i) int(sin^3x-cos^3x)/(sin^...

Evaluate:
(i) `int(sin^3x-cos^3x)/(sin^2xcos^2x)\ dx`
(ii) `int(5cos^3x+6sin^3x)/(2sin^2xcos^2x)\ dx`

Text Solution

Verified by Experts


(i) `int(sin^3x-cos^3x)/(sin^2xcos^2x)\ dx`

`=int(tanx secx-cotx cosex) dx`

`=secx+cosecx+C`


(ii) `int(5cos^3x+6sin^3x)/(2sin^2xcos^2x)\ dx`

`=(5/2)int(cotx cosex)\dx+3int(tanx secx)\dx`

`=(-5/2)(cosecx)+3secx+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

int(5cos^3x+7sin^3x)/(sin^2xcos^2x)dx

int(5cos^3x+7sin^3x)/(3sin^2xcos^2x)dx

int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx

Find int(sin^3x+cos^3x)/(sin^2xcos^2x)dx .

int(sin^(3)x-cos^(3)x)/(sin^(2)x cos^(2)x)dx

int(3sin^(3)x+cos^(3)x)/(sin^(2)xcos^(2)x)dx=

Evaluate: int(sin x cos x)/(3sin^(2)x-4cos^(2)x)dx

int(sin2xcos2x)/(sin^(4)2x+cos^(4)2x)dx=

int(sin^(2)x-cos^(2)x)/(sin^(2)xcos^(2)x)dx=

RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: (i) int(x^5+x^(-2)+2)/(x^2)\ dx (ii) int(5\ x^4+12\ x^3+7...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  20. Evaluate: (i) inte^(2x-3)\ dx (ii) inta^(3x+2)\ dx

    Text Solution

    |