Sr Examen
Integral de 1/(x(sqrt(x+2))) dx
Solución
Ha introducido
[src]
7 / | | 1 | ----------- dx | _______ | x*\/ x + 2 | / 2
$$\int\limits_{2}^{7} \frac{1}{x \sqrt{x + 2}}\, dx$$
Integral(1/(x*sqrt(x + 2)), (x, 2, 7))
Respuesta (Indefinida)
[src]
// / ___ _______\ \ / || ___ |\/ 2 *\/ 2 + x | |2 + x| | | ||-\/ 2 *acoth|---------------| for ------- > 1| | 1 || \ 2 / 2 | | ----------- dx = C + |< | | _______ || / ___ _______\ | | x*\/ x + 2 || ___ |\/ 2 *\/ 2 + x | | | ||-\/ 2 *atanh|---------------| otherwise | / \\ \ 2 / /
$$\int \frac{1}{x \sqrt{x + 2}}\, dx = C + \begin{cases} - \sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} & \text{for}\: \frac{\left|{x + 2}\right|}{2} > 1 \\- \sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \sqrt{x + 2}}{2} \right)} & \text{otherwise} \end{cases}$$
Gráfica
Respuesta
[src]
/ ___\
___ / ___\ ___ |3*\/ 2 |
\/ 2 *acoth\\/ 2 / - \/ 2 *acoth|-------|
\ 2 /
$$- \sqrt{2} \operatorname{acoth}{\left(\frac{3 \sqrt{2}}{2} \right)} + \sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \right)}$$
=
=
/ ___\
___ / ___\ ___ |3*\/ 2 |
\/ 2 *acoth\\/ 2 / - \/ 2 *acoth|-------|
\ 2 /
$$- \sqrt{2} \operatorname{acoth}{\left(\frac{3 \sqrt{2}}{2} \right)} + \sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \right)}$$
sqrt(2)*acoth(sqrt(2)) - sqrt(2)*acoth(3*sqrt(2)/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.