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Math Help - Evaluating indefinite integral thread number 1?

  1. #1
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    Evaluating indefinite integral thread number 1?

    Can anyone help me integrate the following functions

    1.((x^2+x+1))/((square root(x))

    The square root on the denominator is confusing me.

    2. ((1-csc(x) times cot(x))

    Any help would be appreciated
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  2. #2
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    Re: Evaluating indefinite integral thread number 1?

    1. Use the fact that \dfrac{a+b+c}{d} = \dfrac{a}{d} + \dfrac{b}{d} +\dfrac{c}{d}. This will give you three terms to integrate which can be done separately using the power rule
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    Re: Evaluating indefinite integral thread number 1?

    1. \int\frac{x^2+x+1}{\sqrt(x)}dx=\int\frac{x^2}{\sqr  t(x)}+\frac{x}{\sqrt(x)}+\frac{1}{\sqrt(x)}dx

    2. \int\cot{x}dx=\ln{\sin(x) and \int\csc{x}\cot{x}dx=-\csc{x}
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    Re: Evaluating indefinite integral thread number 1?

    For my first question I have

    ((x^2))/square root(x)+(x)/square root(x)+1/square root(x)

    Would anyone kindly help me integrate this.
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Re: Evaluating indefinite integral thread number 1?

    Quote Originally Posted by homeylova223 View Post
    For my first question I have

    ((x^2))/square root(x)+(x)/square root(x)+1/square root(x)

    Would anyone kindly help me integrate this.
    Read here first:

    Exponentiation - Wikipedia, the free encyclopedia

    then, here:

    http://www.tech.plym.ac.uk/maths/res..._integrals.pdf
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    Re: Evaluating indefinite integral thread number 1?

    \frac{x^2}{\sqrt(x)}=x^\frac{3}{2} now use power rule to integrate
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    Re: Evaluating indefinite integral thread number 1?

    @Homeylova223:
    It's really important you can work with powers and exponents etc ... so you have to know the basic rules, like: a^{x}\cdot a^{y}=a^{x+y}, etc...
    Take a look at the site Also sprach Zarathrusta has given you.
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  8. #8
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    Re: Evaluating indefinite integral thread number 1?

    How do you know that ((x^2))/((square root(x))= x^(3/2)

    Would you kindly show me? Because I have never done this type of intergral problem before and my textbook does not cover it.

    I read the wiki but can anyone just help with this specific problem please.

    Wait I think I understand do I use this rule (a^n)/(a^m)

    a^n-a^m?
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: Evaluating indefinite integral thread number 1?

    Because:
    \frac{x^2}{\sqrt{x}} =\frac{x^2}{x^{\frac{1}{2}}} =x^{2-\frac{1}{2}}=x^{\frac{3}{2}}

    This is what I meant with the fact you've to know the basic rules ...

    EDIT:
    Can you calculate the primitive function now?
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  10. #10
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    Re: Evaluating indefinite integral thread number 1?

    I think I can evaluate it I have

    x^(3/2)+x^(1/2)+x^(-1/2)

    (2/5)x^(5/2)+(2/3)x^(1/2)+2x^(1/2)?
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  11. #11
    MHF Contributor Siron's Avatar
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    Re: Evaluating indefinite integral thread number 1?

    You made a little mistake in the exponent of the second term, the primitive function has to be:
    F(x)=\frac{2}{5}\cdot x^{\frac{5}{2}}+\frac{2}{3}\cdot x^{\frac{3}{2}}+2\cdot x^{\frac{1}{2}}+C
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