Always do long division first when the degree of $\mathrm{f}(x)\ge $ degree of $\mathrm{g}(x)$ f

Question

Always do long division first when the degree of $\mathrm{f}(x)\ge $ degree of $\mathrm{g}(x)$ for $\displaystyle \displaystyle\int{\frac{\mathrm{f}\left( x \right)}{\mathrm{g}\left( x \right)}\,\mathrm{d}x}$

$\displaystyle\displaystyle \displaystyle\int{\frac{{{x}^{4}}-{{x}^{2}}+x}{{{x}^{3}}+1}}dx$

Accepted Answer

$\frac{x^2}2-\frac13\ln|x^3+1|+C$

Techniques of Integration - Integrals Involving Long Division

Techniques of Integration - Integrals Involving Long Division

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