Tavola degli integrali indefiniti di funzioni irrazionali: differenze tra le versioni
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m r2.7.3) (Bot: Aggiungo ta:விகிதமுறா சார்புகளின் தொகையீடுகளின் பட்டியல் |
Adeguamento alle norme ISO per le funzioni iperboliche (settsinh --> arsinh etc.), cfr http://it.wikipedia.org/wiki/Funzioni_iperboliche#Notazioni |
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Riga 11:
: <math>\int\frac{x^2\;dx}{\sqrt{a^2-x^2}} = -\frac{x}{2}\sqrt{a^2-x^2}+\frac{a^2}{2}\arcsin\frac{x}{a} \qquad\mbox{(}|x|\leq|a|\mbox{)}</math>
: <math>\int\sqrt{x^2+a^2}\;dx = \frac{1}{2}\left(x\sqrt{x^2+a^2}+a^2\,\mathrm{
: <math>\int x\sqrt{x^2+a^2}\;dx=\frac{1}{3}\sqrt{(x^2+a^2)^3}</math>
Riga 17:
: <math>\int\frac{\sqrt{x^2+a^2}\;dx}{x} = \sqrt{x^2+a^2}-a\log\left|\frac{a+\sqrt{x^2+a^2}}{x}\right|</math>
: <math>\int\frac{dx}{\sqrt{x^2+a^2}} = \mathrm{
: <math>\int\frac{x\,dx}{\sqrt{x^2+a^2}} = \sqrt{x^2+a^2}</math>
: <math>\int\frac{x^2\;dx}{\sqrt{x^2+a^2}} = \frac{x}{2}\sqrt{x^2+a^2}-\frac{a^2}{2}\,\mathrm{
: <math>\int\frac{dx}{x\sqrt{x^2+a^2}} = -\frac{1}{a}\,\mathrm{
: <math>\int\sqrt{x^2-a^2}\;dx = \frac{1}{2}\left(x\sqrt{x^2-a^2}\mp a^2\,\mathrm{
: <math>\int x\sqrt{x^2-a^2}\;dx = \frac{1}{3}\sqrt{(x^2-a^2)^3} \qquad\mbox{(per }|x|\ge|a|\mbox{)}</math>
Riga 31:
: <math>\int\frac{\sqrt{x^2-a^2}\;dx}{x} = \sqrt{x^2-a^2} - a\arcsin\frac{a}{x} \qquad\mbox{(per }|x|\ge|a|\mbox{)}</math>
: <math>\int\frac{dx}{\sqrt{x^2-a^2}} = \mathrm{
: <math>\int\frac{x\;dx}{\sqrt{x^2-a^2}} = \sqrt{x^2-a^2} \qquad\mbox{(per }|x|>|a|\mbox{)}</math>
: <math>\int\frac{x^2\,dx}{\sqrt{x^2-a^2}} = \frac{x}{2}\sqrt{x^2-a^2}+\frac{a^2}{2}\,\mathrm{
: <math>\int\frac{dx}{\sqrt{ax^2+bx+c}} = \frac{1}{\sqrt{a}}\ln\left|2\sqrt{a(ax^2+bx+c)}+2ax+b\right| \qquad\mbox{(per }a>0\mbox{)}</math>
: <math>\int\frac{dx}{\sqrt{ax^2+bx+c}} = \frac{1}{\sqrt{a}}\,\mathrm{
: <math>\int\frac{dx}{\sqrt{ax^2+bx+c}} = \frac{1}{\sqrt{a}}\log|2ax+b| \qquad\mbox{(per }a>0\mbox{, }4ac-b^2=0\mbox{)}</math>
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