Sr Examen
Integral de dx/x^3*(sqrt(x-8)) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ x - 8 | --------- dx | 3 | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x - 8}}{x^{3}}\, dx$$
Integral(sqrt(x - 8)/x^3, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ _______\ \
| |\/ 2 *\/ x - 8 | | / / ___ _______\ \
|3*atan|---------------| ___ _______ ___ _______ | | |\/ 2 *\/ x - 8 | |
/ ___ | \ 4 / \/ 2 *\/ x - 8 \/ 2 *\/ x - 8 *(16 - x)| |atan|---------------| ___ _______|
| \/ 2 *|----------------------- + --------------- + ------------------------| ___ | \ 4 / \/ 2 *\/ x - 8 |
| _______ | 8 x 2 | \/ 2 *|--------------------- + ---------------|
| \/ x - 8 \ 4*x / \ 2 x /
| --------- dx = C - ---------------------------------------------------------------------------- + -----------------------------------------------
| 3 16 16
| x
|
/
$$\int \frac{\sqrt{x - 8}}{x^{3}}\, dx = C + \frac{\sqrt{2} \left(\frac{\operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{x - 8}}{4} \right)}}{2} + \frac{\sqrt{2} \sqrt{x - 8}}{x}\right)}{16} - \frac{\sqrt{2} \left(\frac{3 \operatorname{atan}{\left(\frac{\sqrt{2} \sqrt{x - 8}}{4} \right)}}{8} + \frac{\sqrt{2} \sqrt{x - 8}}{x} + \frac{\sqrt{2} \left(16 - x\right) \sqrt{x - 8}}{4 x^{2}}\right)}{16}$$
Gráfica
Respuesta
[src]
1 / | | ________ | \/ -8 + x | ---------- dx | 3 | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x - 8}}{x^{3}}\, dx$$
=
=
1 / | | ________ | \/ -8 + x | ---------- dx | 3 | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x - 8}}{x^{3}}\, dx$$
Integral(sqrt(-8 + x)/x^3, (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.