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Math Help - Undefinite Integral Question

  1. #1
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    Undefinite Integral Question

    I want to know if :

    \int [cos(x)\cdot e^{2sin(x))}+\pi \cdot cos(4x)+\sqrt{2}\cdot x^{1/3}+\frac{1}{x}] dx

    is equal to :

    {\int cos(x)dx} \cdot {\int e^{2sin(x)}dx} + {\int \pi \cdot cos(4x)dx+{\int \sqrt{2}}}\cdot {x^{1/3}dx}+{\int \frac {1}{x}}dx

    and if it is not , how can i solve this indefinite integral
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  2. #2
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    Quote Originally Posted by Larrioto View Post
    I want to know if :

    \int [cos(x)\cdot e^{2sin(x))}+\pi \cdot cos(4x)+\sqrt{2}\cdot x^{1/3}+\frac{1}{x}] dx

    is equal to :

    {\int cos(x)dx} \cdot {\int e^{2sin(x)}dx} + {\int \pi \cdot cos(4x)dx+{\int \sqrt{2}}}\cdot {x^{1/3}dx}+{\int \frac {1}{x}}dx

    and if it is not , how can i solve this indefinite integral
    No, not quite. It's equal to:

    {\int cos(x)e^{2sin(x)}\,dx} + {\int \pi \cdot cos(4x)dx+{\int \sqrt{2}}}\cdot {x^{1/3}dx}+{\int \frac {1}{x}}dx

    You can do the first term by substitution. Notice that cos(x) is the derivative of sin(x).

     u = sin(x)

     \frac{du}{dx} = cos(x)

     du = cos(x)dx

    {\int e^{2u}\,du} + \pi {\int  cos(4x)dx+\sqrt{2}{\int }}\cdot {x^{1/3}dx}+{\int x^{-1}}dx
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  3. #3
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    would the answer be :

    \frac {e^{2cos(x)}}{2}+\pi \cdot(\frac {-sin{4x}}{4})+\sqrt{2}\cdot \frac{(3x^{\frac{4}{3}})}{4}+ln|x|
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  4. #4
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    Quote Originally Posted by Larrioto View Post
    would the answer be :

    \frac {e^{2cos(x)}}{2}+\pi \cdot(\frac {-sin{4x}}{4})+\sqrt{2}\cdot \frac{(3x^{\frac{4}{3}})}{4}+ln|x|
    i think the final answer would be this:



    \frac {e^{2sen(x)}}{2}+\pi \cdot(\frac {sin{4x}}{4})+\sqrt{2}\cdot \frac{(3x^{\frac{4}{3}})}{4}+ln|x|<br />
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  5. #5
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    Quote Originally Posted by PanZerOlas View Post
    i think the final answer would be this:



    \frac {e^{2sen(x)}}{2}+\pi \cdot(\frac {sin{4x}}{4})+\sqrt{2}\cdot \frac{(3x^{\frac{4}{3}})}{4}+ln|x|<br />
    Thank you
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