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