If \[\int{\frac{(2{{x}^{2}}+1)\,\,dx}{({{x}^{2}}-4)\,\,({{x}^{2}}-1)}=\log \left[ {{\left( \frac{x+1}{x-1} \right)}^{a}}\,\,{{\left( \frac{x-2}{x+2} \right)}^{b}} \right]}+C,\] then the values of a and b are respectively [Roorkee 2000]

If \[\int{\frac{(2{{x}^{2}}+1)\,\,dx}{({{x}^{2}}-4)\,\,({{x}^{2}}-1)}=

1.	If \[\int{\frac{(2{{x}^{2}}+1)\,\,dx}{({{x}^{2}}-4)\,\,({{x}^{2}}-1)}=\log \left[ {{\left( \frac{x+1}{x-1} \right)}^{a}}\,\,{{\left( \frac{x-2}{x+2} \right)}^{b}} \right]}+C,\] then the values of a and b are respectively [Roorkee 2000]
A.	1/2, ¾
B.	-1, 3/2
C.	1, 3/2
D.	-1/2, ¾
Answer» B. -1, 3/2

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If \[\int{\frac{(2{{x}^{2}}+1)\,\,dx}{({{x}^{2}}-4)\,\,({{x}^{2}}-1)}=\log \left[ {{\left( \frac{x+1}{x-1} \right)}^{a}}\,\,{{\left( \frac{x-2}{x+2} \right)}^{b}} \right]}+C,\] then the values of a and b are respectively [Roorkee 2000]

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