Razlike između izmjena na stranici "Popis integrala racionalnih funkcija"

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|<math>\int\frac{1}{x^2-a^2} dx = </math>||
* <math> -\frac{1}{a}\,\mathrm{arctanh}\frac{x}{a} = \frac{1}{2a}\ln\frac{a-x}{a+x} \qquad\mbox{(za }|x| < |a|\mbox{)}\,\!</math>
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* <math> -\frac{1}{a}\,\mathrm{arccoth}\frac{x}{a} = \frac{1}{2a}\ln\frac{x-a}{x+a} \qquad\mbox{(za }|x| > |a|\mbox{)}\,\!</math>
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|<math>\int\frac{1}{ax^2+bx+c} dx =</math>||
* <math> \frac{2}{\sqrt{4ac-b^2}}\arctan\frac{2ax+b}{\sqrt{4ac-b^2}} \qquad\mbox{(za }4ac-b^2>0\mbox{)}</math>
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* <math> -\frac{2}{\sqrt{b^2-4ac}}\,\mathrm{arctanh}\frac{2ax+b}{\sqrt{b^2-4ac}} = \frac{1}{\sqrt{b^2-4ac}}\ln\left|\frac{2ax+b-\sqrt{b^2-4ac}}{2ax+b+\sqrt{b^2-4ac}}\right| \qquad\mbox{(za }4ac-b^2<0\mbox{)}</math>
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* <math> -\frac{2}{2ax+b}\qquad\mbox{(za }4ac-b^2=0\mbox{)}</math>
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|<math>\int\frac{x}{ax^2+bx+c} dx</math>||<math> = \frac{1}{2a}\ln\left|ax^2+bx+c\right|-\frac{b}{2a}\int\frac{dx}{ax^2+bx+c}</math>
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|<math>\int\frac{mx+n}{ax^2+bx+c} dx = </math> ||
* <math>\frac{m}{2a}\ln\left|ax^2+bx+c\right|+\frac{2an-bm}{a\sqrt{4ac-b^2}}\arctan\frac{2ax+b}{\sqrt{4ac-b^2}} \qquad\mbox{(za }4ac-b^2>0\mbox{)}</math>
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* <math>\frac{m}{2a}\ln\left|ax^2+bx+c\right|+\frac{2an-bm}{a\sqrt{b^2-4ac}}\,\mathrm{artanh}\frac{2ax+b}{\sqrt{b^2-4ac}} \qquad\mbox{(za }4ac-b^2<0\mbox{)}</math>
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* <math> \frac{m}{2a}\ln\left|ax^2+bx+c\right|-\frac{2an-bm}{a(2ax+b)} \,\,\,\,\,\,\,\,\,\, \qquad\mbox{(za }4ac-b^2=0\mbox{)}</math>
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