Friday, 16 March 2018

integration - Error in intlimitsinfty0dx,fraclog2xa2+x2



This is my work for solving the improper integralI=0dxlog2xx2+a2

I feel like I did everything write, but when I substitute values into a, it doesn’t match up with Wolfram Alpha.






First substitute x=a2u soI=0du2log2alog2ux2+a2=0du2log2aa2+x20dulog2ua2+x2

HenceI=0dulog2aa2+x2=log2aa2π/20dtasec2t1+tan2t=πlog2a2a
However, when a=e Wolfram Alpha evaluates the integral numerically asI2.00369
however the input that I arrived at evaluates numericallyπ2e0.5778
Where did I go wrong? And how would you go about solving this integral?


Answer



Note
log2(a2u)2log2alog2u.



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