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Math Help - Found Answer but Wondering how, more integration

  1. #1
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    Found Answer but Wondering how, more integration

    <br />
\int {(15sinx+6tanx)}dx<br />

    So I broke it up

    <br />
15 \int {sinx} + 6 \int {tanx}<br />

    Then got...

    <br />
{-15cosx-6ln|cosx|}<br />

    I know its right however I don't know if I was taught the integral of tanx, so I was wondering if there was any other way of doing it?
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  2. #2
    Super Member General's Avatar
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    Quote Originally Posted by Lolcats View Post
    <br />
\int {(15sinx+6tanx)}dx<br />

    So I broke it up

    <br />
15 \int {sinx} + 6 \int {tanx}<br />

    Then got...

    <br />
{-15cosx-6ln|cosx|}<br />

    I know its right however I don't know if I was taught the integral of tanx, so I was wondering if there was any other way of doing it?
    Its the ideal solution.
    And you should have {\color{red}+C}.
    and -15cos(x)-6ln|cos(x)|+C=-15cos(x)+6ln|sec(x)|+C.

    I do not know what is the point of seraching for another solutions ?
    Last edited by General; January 17th 2010 at 03:35 PM.
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  3. #3
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    Its not peticularly finding other solutions just the way of getting to it, or is that the only way?
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  4. #4
    Super Member General's Avatar
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    Quote Originally Posted by Lolcats View Post
    Its not peticularly finding other solutions just the way of getting to it, or is that the only way?
    The integral of sine is known.
    The integral of tan is known.
    then the integral of thier sum is known.
    If you looking for another solutions, you can consider thier maclaurin series.
    but this will make it complicated.

    In other words, What is the integral of \int x dx ?
    It is \frac{x^2}{2} + C .
    That is !
    Whatever you do, you will get the same answer in different shapes.
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  5. #5
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    Ah k alright thank you!
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