搜尋結果
Hyperbolic functions occur in the calculations of angles and distances in hyperbolic geometry. It also occurs in the solutions of many linear differential equations (such as the equation defining a catenary), cubic equations, and Laplace's equation in Cartesian coordinates.
Principal values. Since none of the six trigonometric functions are one-to-one, they must be restricted in order to have inverse functions. Therefore, the result ranges of the inverse functions are proper (i.e. strict) subsets of the domains of the original functions.
- Arcsine Function Integration Formulas
- Arccosine Function Integration Formulas
- Arctangent Function Integration Formulas
- Arccotangent Function Integration Formulas
- Arcsecant Function Integration Formulas
- Arccosecant Function Integration Formulas
- See Also
∫ arcsin ( x ) d x = x arcsin ( x ) + 1 − x 2 + C {\displaystyle \int \arcsin(x)\,dx=x\arcsin(x)+{\sqrt {1-x^{2}}}+C} ∫ arcsin ( a x ) d x = x arcsin ( a x ) + 1 − a 2 x 2 a + C {\displaystyle \int \arcsin(ax)\,dx=x\arcsin(ax)+{\frac {\sqrt {1-a^{2}x^{2}}}{a}}+C} ∫ x arcsin ( a x ) d x = x 2 arcsin ( a x ) 2 − arcsin ( a x ) 4 a 2 + x...
∫ arccos ( x ) d x = x arccos ( x ) − 1 − x 2 + C {\displaystyle \int \arccos(x)\,dx=x\arccos(x)-{\sqrt {1-x^{2}}}+C} ∫ arccos ( a x ) d x = x arccos ( a x ) − 1 − a 2 x 2 a + C {\displaystyle \int \arccos(ax)\,dx=x\arccos(ax)-{\frac {\sqrt {1-a^{2}x^{2}}}{a}}+C} ∫ x arccos ( a x ) d x = x 2 arccos ( a x ) 2 − arccos ( a x ) 4 a 2 − x...
∫ arctan ( x ) d x = x arctan ( x ) − ln ( x 2 + 1 ) 2 + C {\displaystyle \int \arctan(x)\,dx=x\arctan(x)-{\frac {\ln \left(x^{2}+1\right)}{2}}+C} ∫ arctan ( a x ) d x = x arctan ( a x ) − ln ( a 2 x 2 + 1 ) 2 a + C {\displaystyle \int \arctan(ax)\,dx=x\arctan(ax)-{\frac {\ln \left(a^{2}x^{2}+1\right)}{2\,a}}+C} ∫ x arctan ( a x ) d x...
∫ arccot ( x ) d x = x arccot ( x ) + ln ( x 2 + 1 ) 2 + C {\displaystyle \int \operatorname {arccot}(x)\,dx=x\operatorname {arccot}(x)+{\frac {\ln \left(x^{2}+1\right)}{2}}+C} ∫ arccot ( a x ) d x = x arccot ( a x ) + ln ( a 2 x 2 + 1 ) 2 a + C {\displaystyle \int \operatorname {arccot}(ax)\,dx=x\operatorname {arccot}(ax)+{\frac {\ln \...
∫ arcsec ( x ) d x = x arcsec ( x ) − ln ( | x | + x 2 − 1 ) + C = x arcsec ( x ) − arcosh | x | + C {\displaystyle \int \operatorname {arcsec}(x)\,dx=x\operatorname {arcsec}(x)\,-\,\ln \left(\left|x\right|+{\sqrt {x^{2}-1}}\right)\,+\,C=x\operatorname {arcsec}(x)-\operatorname {arcosh} |x|+C} ∫ arcsec ( a x ) d x = x arcsec ( a x ) −...
∫ arccsc ( x ) d x = x arccsc ( x ) + ln ( | x | + x 2 − 1 ) + C = x arccsc ( x ) + arcosh | x | + C {\displaystyle \int \operatorname {arccsc}(x)\,dx=x\operatorname {arccsc}(x)\,+\,\ln \left(\left|x\right|+{\sqrt {x^{2}-1}}\right)\,+\,C=x\operatorname {arccsc}(x)\,+\,\operatorname {arcosh} |x|\,+\,C} ∫ arccsc ( a x ) d x = x arccsc (...
Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei (/ ˌɡælɪˈleɪoʊ ˌɡælɪˈleɪ /, US also / ˌɡælɪˈliːoʊ -/; Italian: [ɡaliˈlɛːo ɡaliˈlɛːi]), was an Italian (Florentine) [a] astronomer, physicist and engineer, sometimes described as a polymath.
El Niño–Southern Oscillation (ENSO) is a global climate phenomenon that emerges from variations in winds and sea surface temperatures over the tropical Pacific Ocean. Those variations have an irregular pattern but do have some semblance of cycles. The occurrence of ENSO is not predictable.
Antisocial personality disorder (ASPD or APD), sometimes referred to as dissocial personality disorder, is a personality disorder characterized by a limited capacity for empathy and a long-term pattern of disregard for or violation of the rights of others, starting before one was 15 years old. [3][4] Other notable symptoms include impulsivity, r...
Psychopathy, or psychopathic personality, [1] is a personality construct [2][3] characterized by impaired empathy and remorse, and bold, disinhibited and egocentric traits, masked by superficial charm and the outward appearance of apparent normalcy. [4][5][6][7]
