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**superdude** Thanks, finally I get the answer to $\displaystyle \int\frac{x^3+4}{x^2+4} dx$

There's one question I still have: after doing long division I get $\displaystyle \int x - \frac{4x+4}{x^2+4} = \int\frac{4x}{x^2+4}dx+\int\frac{4}{x^2+4}dx != \int-(\frac{4x}{x^2+4}dx+\int\frac{4}{x^2+4}dx)$ where != denotes "not equal" relation. Could someone explain to me why the minus doesn't distrubute over to the second term from the partial fraction? like if it's minus something, and then that something becomes a partial fraction, why wouldn't the second fraction be negative?