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  • Formelsammlung Mathematik: Bestimmte Integrale: Form R(x,log,cos)

    0.1Bearbeiten
    {displaystyle int _{0}^{pi }log left(cos {frac {x}{2}} ight)\,dx=-pi log 2}{displaystyle int _{0}^{pi }log left(cos {frac {x}{2}}
ight)\,dx=-pi log 2}
     
    0.2Bearbeiten
    {displaystyle int _{0}^{frac {pi }{2}}log left(cos {frac {x}{2}} ight)\,dx=G-{frac {pi }{2}}log 2}{displaystyle int _{0}^{frac {pi }{2}}log left(cos {frac {x}{2}}
ight)\,dx=G-{frac {pi }{2}}log 2}
     
    0.3Bearbeiten
    {displaystyle int _{0}^{pi }x^{2}\,log ^{2}left(2cos {frac {x}{2}} ight)\,dx={frac {11pi ^{5}}{180}}}{displaystyle int _{0}^{pi }x^{2}\,log ^{2}left(2cos {frac {x}{2}}
ight)\,dx={frac {11pi ^{5}}{180}}}
     
    0.4Bearbeiten
    {displaystyle int _{0}^{frac {pi }{2}}{frac {x^{2}}{x^{2}+log ^{2}(2cos x)}}\,dx={frac {pi }{8}}left(1-gamma +log 2pi ight)}{displaystyle int _{0}^{frac {pi }{2}}{frac {x^{2}}{x^{2}+log ^{2}(2cos x)}}\,dx={frac {pi }{8}}left(1-gamma +log 2pi 
ight)}
     
    1.1Bearbeiten
    {displaystyle int _{0}^{pi }log left(1-2alpha cos x+alpha ^{2} ight)dx=left{{egin{matrix}0&|alpha |leq 1\\2pi log |alpha |&|alpha |>1end{matrix}} ight.qquad ,qquad alpha in mathbb {R} }{displaystyle int _{0}^{pi }log left(1-2alpha cos x+alpha ^{2}
ight)dx=left{{egin{matrix}0&|alpha |leq 1\\2pi log |alpha |&|alpha |>1end{matrix}}
ight.qquad ,qquad alpha in mathbb {R} }
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  • 原文地址:https://www.cnblogs.com/Eufisky/p/14730817.html
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