Tavola degli integrali indefiniti di funzioni trigonometriche: differenze tra le versioni
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Riga 16:
: <math>\int x^n\sin (cx)\;\mathrm {d} x = -\frac{x^n}{c}\cos cx+\frac{n}{c}\int x^{n-1}\cos cx\;\mathrm {d} x \qquad\mbox{(per }n>0\mbox{)}</math>
: <math>\int\frac{\sin (cx)}{x} \mathrm {d} x = \sum_{i=0}^\infty (-1)^i\frac{(cx)^{2i+1}}{(2i+1)\cdot (2i+1)!}</math>
: <math>\int\frac{\sin (cx)}{x^n} \mathrm {d} x = -\frac{\sin cx}{(n-1)x^{n-1}} + \frac{c}{n-1}\int\frac{\cos (cx)}{x^{n-1}} \mathrm {d} x</math>
: <math>\int\frac{\mathrm {d} x}{\sin (cx)} = \frac{1}{c}\ln \left|\tan\frac{cx}{2}\right|</math>
: <math>\int\frac{\mathrm {d} x}{\sin^n (cx)} = \frac{\cos (cx)}{c(1-n) \sin^{n-1} (cx)}+\frac{n-2}{n-1}\int\frac{\mathrm {d} x}{\sin^{n-2}cx} \qquad\mbox{(per }n>1\mbox{)}</math>
: <math>\int\frac{\mathrm {d} x}{1\pm\sin (cx)} = \frac{1}{c}\tan\left(\frac{cx}{2}\mp\frac{\pi}{4}\right)</math>
: <math>\int\frac{x\;\mathrm {d} x}{1+\sin (cx=} = \frac{x}{c}\tan\left(\frac{cx}{2} - \frac{\pi}{4}\right)+\frac{2}{c^2}\ln\left|\cos\left(\frac{cx}{2}-\frac{\pi}{4}\right)\right|</math>
: <math>\int\frac{x\;\mathrm {d} x}{1-\sin cx} = \frac{x}{c}\cot\left(\frac{\pi}{4} - \frac{cx}{2}\right)+\frac{2}{c^2}\ln\left|\sin \left(\frac{\pi}{4}-\frac{cx}{2}\right)\right|</math>
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