Sr Examen
Integral de Sgrt(5x^2-4)^3 dx
Solución
Ha introducido
[src]
3 / | | 3 | __________ | / 2 | \/ 5*x - 4 dx | / 0
$$\int\limits_{0}^{3} \left(\sqrt{5 x^{2} - 4}\right)^{3}\, dx$$
Integral((sqrt(5*x^2 - 4))^3, (x, 0, 3))
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___ |x*\/ 5 | |
|| 3 2*\/ 5 *acosh|-------| 5 | 2| |
/ || 3*x \ 2 / 2*x 5*x 5*|x | |
| ||- ---------------- - ---------------------- + ---------------- + ---------------- for ------ > 1| / ___\
| 3 || ___________ 25 ___________ ___________ 4 | ___ |x*\/ 5 |
| __________ || / 2 / 2 / 2 | ___________ 8*\/ 5 *acosh|-------|
| / 2 || 2*\/ -4 + 5*x 5*\/ -4 + 5*x 4*\/ -4 + 5*x | / 2 \ 2 /
| \/ 5*x - 4 dx = C + 5*|< | - 2*x*\/ -4 + 5*x + ----------------------
| || / ___\ | 5
/ || ___ |x*\/ 5 | |
|| 5 2*I*\/ 5 *asin|-------| 3 |
|| 5*I*x 2*I*x \ 2 / 3*I*x |
|| - --------------- - --------------- + ----------------------- + --------------- otherwise |
|| __________ __________ 25 __________ |
|| / 2 / 2 / 2 |
\\ 4*\/ 4 - 5*x 5*\/ 4 - 5*x 2*\/ 4 - 5*x /
$$\int \left(\sqrt{5 x^{2} - 4}\right)^{3}\, dx = C - 2 x \sqrt{5 x^{2} - 4} + 5 \left(\begin{cases} \frac{5 x^{5}}{4 \sqrt{5 x^{2} - 4}} - \frac{3 x^{3}}{2 \sqrt{5 x^{2} - 4}} + \frac{2 x}{5 \sqrt{5 x^{2} - 4}} - \frac{2 \sqrt{5} \operatorname{acosh}{\left(\frac{\sqrt{5} x}{2} \right)}}{25} & \text{for}\: \frac{5 \left|{x^{2}}\right|}{4} > 1 \\- \frac{5 i x^{5}}{4 \sqrt{4 - 5 x^{2}}} + \frac{3 i x^{3}}{2 \sqrt{4 - 5 x^{2}}} - \frac{2 i x}{5 \sqrt{4 - 5 x^{2}}} + \frac{2 \sqrt{5} i \operatorname{asin}{\left(\frac{\sqrt{5} x}{2} \right)}}{25} & \text{otherwise} \end{cases}\right) + \frac{8 \sqrt{5} \operatorname{acosh}{\left(\frac{\sqrt{5} x}{2} \right)}}{5}$$
Gráfica
Respuesta
[src]
/ ___\
___ |3*\/ 5 |
____ 6*\/ 5 *acosh|-------| ___
105*\/ 41 \ 2 / 3*pi*I*\/ 5
---------- + ---------------------- - ------------
4 5 5
$$\frac{6 \sqrt{5} \operatorname{acosh}{\left(\frac{3 \sqrt{5}}{2} \right)}}{5} + \frac{105 \sqrt{41}}{4} - \frac{3 \sqrt{5} i \pi}{5}$$
=
=
/ ___\
___ |3*\/ 5 |
____ 6*\/ 5 *acosh|-------| ___
105*\/ 41 \ 2 / 3*pi*I*\/ 5
---------- + ---------------------- - ------------
4 5 5
$$\frac{6 \sqrt{5} \operatorname{acosh}{\left(\frac{3 \sqrt{5}}{2} \right)}}{5} + \frac{105 \sqrt{41}}{4} - \frac{3 \sqrt{5} i \pi}{5}$$
105*sqrt(41)/4 + 6*sqrt(5)*acosh(3*sqrt(5)/2)/5 - 3*pi*i*sqrt(5)/5
Respuesta numérica
[src]
(173.127377494368 - 4.21498218050726j)
(173.127377494368 - 4.21498218050726j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.