Evaluate $\backslash$int $(7$x$^(2)+3$x$-1)/(2$x$^(3)+3$x$^(2)-2$x$)$dx

Solution

Since the degree of the numerator is less than the degree of the denominator, we don't need to divide. We factor the denominator as

$2$x$3+3$x$22$x $=$ x$(2$x$2+3$x $2)=$ x$(2$x $1)($x $+2).$

Since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the following form $[$see this case$].$