Questions in indefinite-integration

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$\int_{{}}^{{}}{\frac{dx}{x[{{(\log x)}^{2}}+4\log x-1]}}=$
$\int_{{}}^{{}}{\frac{dx}{x({{x}^{n}}+1)}=}$
$\int_{{}}^{{}}{\frac{dx}{x({{x}^{7}}+1)}}=$
$\int_{{}}^{{}}{\frac{dx}{x({{x}^{5}}+1)}}=$
$\int_{{}}^{{}}{\frac{{{x}^{2}}+1}{{{x}^{4}}+1}dx=}$
$\int_{{}}^{{}}{\frac{{{x}^{2}}-1}{{{x}^{4}}+{{x}^{2}}+1}\ dx=}$
$\int{\frac{x\,\,dx}{{{x}^{2}}+4x+5}=}$
If $\int{\frac{2{{x}^{2}}+3.dx}{({{x}^{2}}-1)({{x}^{2}}-4)}}=\log {{\left( \frac{x-2}{x+2} \right)}^{a}}{{\left( \frac{x+1}{x-1} \right)}^{b}}+c$ then the values of a and b respectively are

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