Sr Examen
Integral de sqrt(1+coshx) dx
Solución
Ha introducido
[src]
1/2 / | | _____________ | \/ 1 + cosh(x) dx | / -1/2
$$\int\limits_{- \frac{1}{2}}^{\frac{1}{2}} \sqrt{\cosh{\left(x \right)} + 1}\, dx$$
Integral(sqrt(1 + cosh(x)), (x, -1/2, 1/2))
Respuesta (Indefinida)
[src]
_________________________________
/ / 2/x\
| / tanh |-|
| _____________ / 1 \2/ /x\
| \/ 1 + cosh(x) dx = C + 2* / 1 + ------------ + ------------ *tanh|-|
| / 2/x\ 2/x\ \2/
/ / 1 - tanh |-| 1 - tanh |-|
\/ \2/ \2/
$$\int \sqrt{\cosh{\left(x \right)} + 1}\, dx = C + 2 \sqrt{1 + \frac{\tanh^{2}{\left(\frac{x}{2} \right)}}{1 - \tanh^{2}{\left(\frac{x}{2} \right)}} + \frac{1}{1 - \tanh^{2}{\left(\frac{x}{2} \right)}}} \tanh{\left(\frac{x}{2} \right)}$$
Gráfica
Respuesta
[src]
_____________________________________
/ 2
/ 1 tanh (1/4)
4* / 1 + -------------- + -------------- *tanh(1/4)
/ 2 2
\/ 1 - tanh (1/4) 1 - tanh (1/4)
$$4 \sqrt{\frac{\tanh^{2}{\left(\frac{1}{4} \right)}}{1 - \tanh^{2}{\left(\frac{1}{4} \right)}} + 1 + \frac{1}{1 - \tanh^{2}{\left(\frac{1}{4} \right)}}} \tanh{\left(\frac{1}{4} \right)}$$
=
=
_____________________________________
/ 2
/ 1 tanh (1/4)
4* / 1 + -------------- + -------------- *tanh(1/4)
/ 2 2
\/ 1 - tanh (1/4) 1 - tanh (1/4)
$$4 \sqrt{\frac{\tanh^{2}{\left(\frac{1}{4} \right)}}{1 - \tanh^{2}{\left(\frac{1}{4} \right)}} + 1 + \frac{1}{1 - \tanh^{2}{\left(\frac{1}{4} \right)}}} \tanh{\left(\frac{1}{4} \right)}$$
4*sqrt(1 + 1/(1 - tanh(1/4)^2) + tanh(1/4)^2/(1 - tanh(1/4)^2))*tanh(1/4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.