Integral trigonométrica

As integrais trigonométricas são uma família de integrais que envolvem funções trigonométricas. Aqui, apresentamos uma lista de tais integrais:

Seno integral[1][2]

{\rm {Si}}(x)=\int _{0}^{x}{\frac {\sin t}{t}}\,dt,\quad (|x|<\infty )

{\rm {si}}(x)=-\int _{x}^{\infty }{\frac {\sin t}{t}}\,dt={\rm {Si}}(x)-{\frac {1}{2}}\pi ,\quad (|x|<\infty )

Cosseno integral:[1][2]

{\rm {Ci}}(x)=\theta +\ln x+\int _{0}^{x}{\frac {\cos t-1}{t}}\,dt,\quad (0<x<\infty )

,

\theta \approx 0,57722

é a constante de Euler.

{\rm {Cin}}(x)=\int _{0}^{x}{\frac {1-\cos t}{t}}\,dt,\quad (0<x<\infty )

{\rm {ci}}(x)=-\int _{x}^{\infty }{\frac {\cos t}{t}}\,dt,\quad (0<x<\infty )

Seno hiperbólico integral:[2]

{\rm {Shi}}(x)=\int _{0}^{x}{\frac {\sinh t}{t}}\,dt

Co-seno hiperbólico integral:[2]

{\rm {Chi}}(x)=\theta +\ln x+\int _{0}^{x}{\frac {\cosh t-1}{t}}\,dt

{\text{cinh}}(x)=\int _{0}^{x}{\frac {\cosh(t)-1}{t}}dt

Veja também

Referências

ABRAMOWITZ, M.; STEGUN, I.A.; Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematical Series, 1964. ()
Bronshtein, I.N.;; et al. (2007). Handbook of Mathematics 5 ed. [S.l.]: Springer. ISBN 9783540721215

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