Differenze tra le versioni di "Tavola degli integrali indefiniti di funzioni trigonometriche"

{{vedi anche|coseno}}
 
: <math>\int\cos (cx)\;\mathrm {d} x = \frac{1}{c}\sin (cx)}{c}</math>
 
: <math>\int\cos^n (cx)\;\mathrm {d} x = \frac{\cos^{n-1} (cx)\sin (cx)}{nc} + \frac{n-1}{n}\int\cos^{n-2} (cx)\;\mathrm {d} x \qquad\mbox{(per }n>0\mbox{)}</math>
 
: <math>\int x\cos (cx)\;\mathrm {d} x = \frac{\cos (cx)}{c^2} + \frac{x\sin (cx)}{c}</math>
 
: <math>\int x^n\cos (cx)\;\mathrm {d} x = \frac{x^n\sin (cx)}{c} - \frac{n}{c}\int x^{n-1}\sin (cx)\;\mathrm {d} x</math>
 
: <math>\int\frac{\cos (cx)}{x} \mathrm {d} x = \ln|cx|+\sum_{i=1}^\infty (-1)^i\frac{(cx)^{2i}}{2i\cdot(2i)!}</math>
 
: <math>\int\frac{\cos (cx)}{x^n} \mathrm {d} x = -\frac{\cos (cx)}{(n-1)x^{n-1}}-\frac{c}{n-1}\int\frac{\sin (cx)}{x^{n-1}} \mathrm {d} x \qquad\mbox{(per }n\neq 1\mbox{)}</math>
 
: <math>\int\frac{\mathrm {d} x}{\cos (cx)} = \frac{1}{c}\ln\left|\tan\left(\frac{cx}{2}+\frac{\pi}{4}\right)\right|</math>
 
: <math>\int\frac{\mathrm {d} x}{\cos^n (cx)} = \frac{\sin (cx)}{c(n-1) \cos^{n-1} (cx)} + \frac{n-2}{n-1}\int\frac{\mathrm {d} x}{\cos^{n-2} (cx)} \qquad\mbox{(per }n>1\mbox{)}</math>
 
: <math>\int\frac{\mathrm {d} x}{1+\cos (cx)} = \frac{1}{c}\tan\frac{cx}{2}</math>
 
: <math>\int\frac{\mathrm {d} x}{1-\cos (cx)} = -\frac{1}{c}\cot\frac{cx}{2}</math>
 
: <math>\int\frac{x\;\mathrm {d} x}{1+\cos (cx)} = \frac{x}{c}\tan({cx}/{2}) + \frac{2}{c^2}\ln\left|\cos\frac{cx}{2}\right|</math>
 
: <math>\int\frac{x\;\mathrm {d} x}{1-\cos (cx)} = -\frac{x}{x}\cot({cx}/{2})+\frac{2}{c^2}\ln\left|\sin\frac{cx}{2}\right|</math>
 
: <math>\int\frac{\cos cx\;\mathrm {d} x}{1+\cos (cx)} = x - \frac{1}{c}\tan\frac{cx}{2}</math>
 
: <math>\int\frac{\cos cx\;\mathrm {d} x}{1-\cos (cx)} = -x-\frac{1}{c}\cot\frac{cx}{2}</math>
 
: <math>\int\cos c_1x\cos c_2x\;\mathrm {d} x = \frac{\sin(c_1-c_2)x}{2(c_1-c_2)}+\frac{\sin(c_1+c_2)x}{2(c_1+c_2)} \qquad\mbox{(per }|c_1|\neq|c_2|\mbox{)}</math>