Solutions - 0060-02

$$\int \frac{2x^3+3x^2+7x+4}{x+1}dx$$

(1) Numerator degree is not smaller! Long division first:

$$\frac{2x^3+3x^2+7x+4}{x+1}\gg \gg 2x^2+x+6-\frac{2}{x+1}$$

Now this already has the form of a partial fraction decomposition, so we proceed directly to integration.

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(2) Integrate using power rule (with log):

$$\begin{array}{c}\int 2x^2+x+6-\frac{2}{x+1}dx\\ \\ \gg \gg \frac{2}{3}{x}^3+\frac{1}{2}{x}^2+6x-2\ln |x+1|+C\end{array}$$