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