Porisma

A hint to get started

Decompose a linear and irreducible quadratic denominator

Express x2+x(x−1)(x2+1)\frac{x^2+x}{(x-1)(x^2+1)} in the form Ax−1+Bx+Cx2+1\frac A{x-1}+\frac{Bx+C}{x^2+1}. Hence find ∫x2+x(x−1)(x2+1) dx\int\frac{x^2+x}{(x-1)(x^2+1)}\,dx.

CJC · Lecture · Example 8

A quadratic factor requires a general linear numerator Bx+C, even though B turns out to be zero.

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