Find the integral $\int\frac{3x^3-x^2+6x-4}{\left(x^2+1\right)\left(x^2+2\right)}dx$

Find the integral

$\int\frac{dx}{x^2+7x-6}$

Find the integral

$\int \frac { 32 x - 20 } { ( x - 1 ) ( 5 x - 3 ) } d x$

Find the integral

$\int\frac{1}{x\left(x^2+x+1\right)}dx$

Find the integral

$\int\frac{x+7}{x^2+2x-3}dx$

Find the integral

$\int\frac{4}{x^2-4}dx$

Find the integral

$\int\frac{3x-5}{\left(x-1\right)\left(x^2-1\right)}dx$

Find the integral

$\int\frac{4x+12}{\left(x-2\right)\left(x^2+4x+8\right)}dx$