Friday, 23 June 2017

integration - Evaluating the integral intinfty0fracx3x2+a2,mathrmdx



If 0x3x2+a2dx=1ka6, then find the value of k8.




I tried a lot but finally stuck at an intermediate form :



0x3x2+a2dx,withx2=t,2x dx=dt=120(x2)(2x)x2+a2dx=120tt+a2dt=120t+a2a2t+a2dt=12[0dt0a2t+a2dt]=12[t|0a2ln(a2+t)|0]

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