Zerrenda:Integralak: berrikuspenen arteko aldeak
Ezabatutako edukia Gehitutako edukia
61. lerroa:
:<math>\int \cos^n x \, dx = \frac{\cos^{n-1} {x} \sin {x}}{n} + \frac{n-1}{n} \int \cos^{n-2}{x} \, dx</math>
=== Arku-funtzioak (edo alderantzizko funtzio trigonometrikoak) ===
76. lerroa:
:<math>\int \arccsc{x} \, dx = x \, \arccsc{x} + \operatorname{artanh}\,\sqrt{1-\frac{1}{x^2}} + K</math>
=== Funtzio hiperbolikoak ===
:<math>\int \sinh x \, dx = \cosh x + K</math>
:<math>\int \cosh x \, dx = \sinh x + K</math>
:<math>\int \tanh x \, dx = \ln| \cosh x | + K</math>
:<math>\int \mbox{csch}\,x \, dx = \ln\left| \tanh {x \over2}\right| + K</math>
:<math>\int \mbox{sech}\,x \, dx = \arcsin\,(\tanh x) + K</math>
:<math>\int \coth x \, dx = \ln| \sinh x | + K</math>
=== Arku-funtzio hiperbolikoak (edo alderantzizko funtzio hiperbolikoak ===
: <math>\int \operatorname{arsinh} \, x \, dx=
x \, \operatorname{arsinh} \, x-\sqrt{x^2+1}+K</math>
: <math>\int \operatorname{arcosh} \, x \, dx=
x \, \operatorname{arcosh} \, x-\sqrt{x+1} \, \sqrt{x-1}+K</math>
: <math>\int \operatorname{artanh} \, x \, dx=
x \, \operatorname{artanh} \, x+\frac{\ln\left(1-x^2\right)}{2}+K</math>
: <math>\int \operatorname{arcoth} \, x \, dx=
x \, \operatorname{arcoth} \, x+\frac{\ln\left(1-x^2\right)}{2}+K</math>
: <math>\int \operatorname{arsech} \, x \, dx=
x \, \operatorname{arsech} \, x-2 \, \arctan\sqrt{\frac{1-x}{1+x}}+K</math>
: <math>\int \operatorname{arcsch} \, x \, dx=
x \, \operatorname{arcsch} \, x+\operatorname{artanh}\sqrt{\frac{1}{x^2}+1}+K</math>
{{zirriborro}}
| |||