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=12∫∞0(x2)(2x)x2+a2dx=12∫∞0tt+a2dt=12∫∞0t+a2−a2t+a2dt=12[∫∞0dt−∫∞0a2t+a2dt]=12[t|∞0−a2ln(a2+t)|∞0]
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=12∫∞0(x2)(2x)x2+a2dx=12∫∞0tt+a2dt=12∫∞0t+a2−a2t+a2dt=12[∫∞0dt−∫∞0a2t+a2dt]=12[t|∞0−a2ln(a2+t)|∞0]
How to find lim without lhopital rule? I know when I use lhopital I easy get $$ \lim_{h\rightarrow 0}...
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