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  1. #1
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    Smile Integrals_Problems_Avrum

    i have solved many integrals problems , but with these I didn't succseed

    $\displaystyle \int sin(2x-3)dx=$

    $\displaystyle \int \frac{sinx-cosx}{sinx+cosx}dx=$

    $\displaystyle \int \frac{x^5}{x^2+2}dx=$

    $\displaystyle \int a^xe^xdx=$
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  2. #2
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    try for the third

    $\displaystyle
    \int \frac{x^5}{x^2+2}~dx=\int x^3-2x+\frac{4x}{x^2+2}~dx
    $
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  3. #3
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    Quote Originally Posted by gilyos View Post
    i have solved many integrals problems , but with these I didn't succseed

    $\displaystyle \int sin(2x-3)~dx=$
    Note that

    $\displaystyle \int \sin(ax)dx = -\frac{1}{a}\cos(ax)+C$
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  4. #4
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    Consider

    $\displaystyle \frac{\sin(x) - \cos(x) }{ \sin(x) + \cos(x) } = \frac{\tan(x) - 1 }{ \tan(x) + 1 } $


    $\displaystyle = \tan( x - \frac{\pi}{4} ) $
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