Home
Class 12
MATHS
Evaluate the following: (i) int(3xsq...

Evaluate the following:
(i) `int(3xsqrt(x)+4sqrt(x)+5)\ dx`
(ii) `int(2^x+5/x-1/(x^(1//3)))\ dx`

Text Solution

Verified by Experts

(i) `=int(3xsqrt(x)+4sqrt(x)+5)\ dx`

`=int(3x^(3/2)+4x^(1/2)+5)\dx`

`=(3x^(5/2))/(5/2)+(4x^(3/2))/(3/2)+5x+C`

`=(6x^(5/2))/(5)+(8x^(3/2))/(3)+5x+C`


(ii) `=int(2^x+5/x-1/(x^(1//3)))\ dx`

...
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(x.sqrt(x-5)) dx

Evaluate the following: (i) int sqrt(1+sin((1)/(2)x))dx (ii) int(x^(2))/(sqrt(1-x))dx

int(1)/(sqrt(x)+x4)dx( ii) int(1)/(x^(1/3)(x^(1/3)-1))dx

Evaluate the following : int_(0)^(1)x.sqrt((1-x^(2))/(1+x^(2)))dx

EXAMPLE 3 -Evaluate the following integrals: (i) int(e^(x)-1)/(e^(x)+1)dx(ii)int(5^(x)+1)/(5^(x)-1)dx

(i) int 2^x/sqrt(1-4^x) dx (ii) int sqrt(e^x-1) dx

Evaluate the following (i) int x log (1+x) dx (ii) int x log^2x dx

Evaluate the following integrals: int(1)/(sqrt(x))dx (ii) int(1)/(x^(3))dx( iii) int a^(3)(log)_(a)x

RD SHARMA-INDEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate: (i) int(x^4+x^2+1)\ d(x^2) (ii) intsin(e^x)d(e^x)

    Text Solution

    |

  2. If f^(prime)(x)=3x^2-2/(x^3) and f(1)=0 , find f(x) .

    Text Solution

    |

  3. Evaluate the following: (i) int(3xsqrt(x)+4sqrt(x)+5)\ dx (ii) in...

    Text Solution

    |

  4. Evaluate: (i) int{sqrt(x)(a x^2+b x+c)}\ dx (ii) int(2-3x)(3+2x)(1-2x...

    Text Solution

    |

  5. Evaluate: int(m/x+x/m+m^x+x^m+m x)\ dx (ii) int(sqrt(x)-1/(sqrt(x)))^2...

    Text Solution

    |

  6. Evaluate: (i) int((1+x)^3)/(sqrt(x))\ dx (ii) int{x^2+e^(logx)+(e/2...

    Text Solution

    |

  7. Evaluate: (i) int(x^e+e^x+e^e)\ dx (ii) intsqrt(x)(x^3-2/x)\ dx

    Text Solution

    |

  8. Evaluate: (i) int1/(sqrt(x))(1+1/x)\ dx (ii) int(x^6+1)/(x^2+1)\ dx

    Text Solution

    |

  9. Evaluate: (i) int(x^(-1//3)+sqrt(x)+2)/(x^3)\ dx (ii) int((1+sqrt(x)...

    Text Solution

    |

  10. Evaluate: (i) intsqrt(x)(3-5x)\ dx (ii) int((x+1)(x-2))/(sqrt(x))\ d...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |