Sr Examen
Integral de acosh(y)*y^2/sqrt(y^2-1) dy
Solución
Ha introducido
[src]
1881 ---- 500 / | | 2 | acosh(y)*y | ----------- dy | ________ | / 2 | \/ y - 1 | / 1
$$\int\limits_{1}^{\frac{1881}{500}} \frac{y^{2} \operatorname{acosh}{\left(y \right)}}{\sqrt{y^{2} - 1}}\, dy$$
Integral((acosh(y)*y^2)/sqrt(y^2 - 1), (y, 1, 1881/500))
Respuesta (Indefinida)
[src]
/ / | | | 2 | 2 | acosh(y)*y | y *acosh(y) | ----------- dy = C + | -------------------- dy | ________ | __________________ | / 2 | \/ (1 + y)*(-1 + y) | \/ y - 1 | | / /
$$\int \frac{y^{2} \operatorname{acosh}{\left(y \right)}}{\sqrt{y^{2} - 1}}\, dy = C + \int \frac{y^{2} \operatorname{acosh}{\left(y \right)}}{\sqrt{\left(y - 1\right) \left(y + 1\right)}}\, dy$$
Gráfica
Respuesta
[src]
2/1881\ _________ /1881\
acosh |----| 1881*\/ 3288161 *acosh|----|
3288161 \500 / \500 /
- ------- + ------------ + ----------------------------
1000000 4 500000
$$- \frac{3288161}{1000000} + \frac{\operatorname{acosh}^{2}{\left(\frac{1881}{500} \right)}}{4} + \frac{1881 \sqrt{3288161} \operatorname{acosh}{\left(\frac{1881}{500} \right)}}{500000}$$
=
=
2/1881\ _________ /1881\
acosh |----| 1881*\/ 3288161 *acosh|----|
3288161 \500 / \500 /
- ------- + ------------ + ----------------------------
1000000 4 500000
$$- \frac{3288161}{1000000} + \frac{\operatorname{acosh}^{2}{\left(\frac{1881}{500} \right)}}{4} + \frac{1881 \sqrt{3288161} \operatorname{acosh}{\left(\frac{1881}{500} \right)}}{500000}$$
-3288161/1000000 + acosh(1881/500)^2/4 + 1881*sqrt(3288161)*acosh(1881/500)/500000
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.