Sr Examen
Integral de 1/(2sh(x)+3ch(x)) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------- dx | 2*sinh(x) + 3*cosh(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{2 \sinh{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx$$
Integral(1/(2*sinh(x) + 3*cosh(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ /x\\
| ___ 3*\/ 5 *tanh|-||
/ ___ |2*\/ 5 \2/|
| 2*\/ 5 *atan|------- + ---------------|
| 1 \ 5 5 /
| --------------------- dx = C + ---------------------------------------
| 2*sinh(x) + 3*cosh(x) 5
|
/
$$\int \frac{1}{2 \sinh{\left(x \right)} + 3 \cosh{\left(x \right)}}\, dx = C + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{x}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
Gráfica
Respuesta
[src]
/ ___\ / ___ ___ \
___ |2*\/ 5 | ___ |2*\/ 5 3*\/ 5 *tanh(1/2)|
2*\/ 5 *atan|-------| 2*\/ 5 *atan|------- + -----------------|
\ 5 / \ 5 5 /
- --------------------- + -----------------------------------------
5 5
$$- \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{5} + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{1}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
=
=
/ ___\ / ___ ___ \
___ |2*\/ 5 | ___ |2*\/ 5 3*\/ 5 *tanh(1/2)|
2*\/ 5 *atan|-------| 2*\/ 5 *atan|------- + -----------------|
\ 5 / \ 5 5 /
- --------------------- + -----------------------------------------
5 5
$$- \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{2 \sqrt{5}}{5} \right)}}{5} + \frac{2 \sqrt{5} \operatorname{atan}{\left(\frac{3 \sqrt{5} \tanh{\left(\frac{1}{2} \right)}}{5} + \frac{2 \sqrt{5}}{5} \right)}}{5}$$
-2*sqrt(5)*atan(2*sqrt(5)/5)/5 + 2*sqrt(5)*atan(2*sqrt(5)/5 + 3*sqrt(5)*tanh(1/2)/5)/5
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.