Seznam integrálů trigonometrických funkcí: Porovnání verzí

m
also -> také
m (also -> také)
: <math>\int\sin^n cx\cos^m cx\;\mathrm{d}x = -\frac{\sin^{n-1} cx\cos^{m+1} cx}{c(n+m)}+\frac{n-1}{n+m}\int\sin^{n-2} cx\cos^m cx\;\mathrm{d}x \qquad\mbox{(pro }m,n>0\mbox{)}\,\!</math>
 
: alsotaké: <math>\int\sin^n cx\cos^m cx\;\mathrm{d}x = \frac{\sin^{n+1} cx\cos^{m-1} cx}{c(n+m)} + \frac{m-1}{n+m}\int\sin^n cx\cos^{m-2} cx\;\mathrm{d}x \qquad\mbox{(pro }m,n>0\mbox{)}\,\!</math>
 
: <math>\int\frac{\mathrm{d}x}{\sin cx\cos cx} = \frac{1}{c}\ln\left|\tan cx\right|</math>
: <math>\int\frac{\sin^n cx\;\mathrm{d}x}{\cos^m cx} = \frac{\sin^{n+1} cx}{c(m-1)\cos^{m-1} cx}-\frac{n-m+2}{m-1}\int\frac{\sin^n cx\;\mathrm{d}x}{\cos^{m-2} cx} \qquad\mbox{(pro }m\neq 1\mbox{)}\,\!</math>
 
: alsotaké: <math>\int\frac{\sin^n cx\;\mathrm{d}x}{\cos^m cx} = -\frac{\sin^{n-1} cx}{c(n-m)\cos^{m-1} cx}+\frac{n-1}{n-m}\int\frac{\sin^{n-2} cx\;\mathrm{d}x}{\cos^m cx} \qquad\mbox{(pro }m\neq n\mbox{)}\,\!</math>
 
: alsotaké: <math>\int\frac{\sin^n cx\;\mathrm{d}x}{\cos^m cx} = \frac{\sin^{n-1} cx}{c(m-1)\cos^{m-1} cx}-\frac{n-1}{n-1}\int\frac{\sin^{n-1} cx\;\mathrm{d}x}{\cos^{m-2} cx} \qquad\mbox{(pro }m\neq 1\mbox{)}\,\!</math>
 
: <math>\int\frac{\cos cx\;\mathrm{d}x}{\sin^n cx} = -\frac{1}{c(n-1)\sin^{n-1} cx} \qquad\mbox{(pro }n\neq 1\mbox{)}\,\!</math>
: <math>\int\frac{\cos^n cx\;\mathrm{d}x}{\sin^m cx} = -\frac{\cos^{n+1} cx}{c(m-1)\sin^{m-1} cx} - \frac{n-m-2}{m-1}\int\frac{cos^n cx\;\mathrm{d}x}{\sin^{m-2} cx} \qquad\mbox{(pro }m\neq 1\mbox{)}\,\!</math>
 
: alsotaké: <math>\int\frac{\cos^n cx\;\mathrm{d}x}{\sin^m cx} = \frac{\cos^{n-1} cx}{c(n-m)\sin^{m-1} cx} + \frac{n-1}{n-m}\int\frac{cos^{n-2} cx\;\mathrm{d}x}{\sin^m cx} \qquad\mbox{(pro }m\neq n\mbox{)}\,\!</math>
 
: alsotaké: <math>\int\frac{\cos^n cx\;\mathrm{d}x}{\sin^m cx} = -\frac{\cos^{n-1} cx}{c(m-1)\sin^{m-1} cx} - \frac{n-1}{m-1}\int\frac{cos^{n-2} cx\;\mathrm{d}x}{\sin^{m-2} cx} \qquad\mbox{(pro }m\neq 1\mbox{)}\,\!</math>
 
== Integrály obsahující [[Sinus|sin]] a [[Tangens|tg]] ==