Sr Examen
Integral de x^2/((sqrt9-x^2)) dx
Solución
Ha introducido
[src]
3/2 / | | 2 | x | ---------- dx | ___ 2 | \/ 9 - x | / 1
$$\int\limits_{1}^{\frac{3}{2}} \frac{x^{2}}{- x^{2} + \sqrt{9}}\, dx$$
Integral(x^2/(sqrt(9) - x^2), (x, 1, 3/2))
Respuesta (Indefinida)
[src]
// / ___\ \
|| ___ |x*\/ 3 | |
/ ||-\/ 3 *acoth|-------| |
| || \ 3 / 2 |
| 2 ||---------------------- for x > 3|
| x || 3 |
| ---------- dx = C - x - 3*|< |
| ___ 2 || / ___\ |
| \/ 9 - x || ___ |x*\/ 3 | |
| ||-\/ 3 *atanh|-------| |
/ || \ 3 / 2 |
||---------------------- for x < 3|
\\ 3 /
$$\int \frac{x^{2}}{- x^{2} + \sqrt{9}}\, dx = C - x - 3 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} x}{3} \right)}}{3} & \text{for}\: x^{2} < 3 \end{cases}\right)$$
Gráfica
Respuesta
[src]
___ /3 ___\ ___ / / 3 ___\\
___ / / ___\\ \/ 3 *log|- + \/ 3 | \/ 3 *|pi*I + log|- - + \/ 3 || ___ / ___\
1 \/ 3 *\pi*I + log\-1 + \/ 3 // \2 / \ \ 2 // \/ 3 *log\1 + \/ 3 /
- - + ------------------------------ + -------------------- - ------------------------------- - --------------------
2 2 2 2 2
$$- \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{2} - \frac{1}{2} + \frac{\sqrt{3} \log{\left(\frac{3}{2} + \sqrt{3} \right)}}{2} - \frac{\sqrt{3} \left(\log{\left(- \frac{3}{2} + \sqrt{3} \right)} + i \pi\right)}{2} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{2}$$
=
=
___ /3 ___\ ___ / / 3 ___\\
___ / / ___\\ \/ 3 *log|- + \/ 3 | \/ 3 *|pi*I + log|- - + \/ 3 || ___ / ___\
1 \/ 3 *\pi*I + log\-1 + \/ 3 // \2 / \ \ 2 // \/ 3 *log\1 + \/ 3 /
- - + ------------------------------ + -------------------- - ------------------------------- - --------------------
2 2 2 2 2
$$- \frac{\sqrt{3} \log{\left(1 + \sqrt{3} \right)}}{2} - \frac{1}{2} + \frac{\sqrt{3} \log{\left(\frac{3}{2} + \sqrt{3} \right)}}{2} - \frac{\sqrt{3} \left(\log{\left(- \frac{3}{2} + \sqrt{3} \right)} + i \pi\right)}{2} + \frac{\sqrt{3} \left(\log{\left(-1 + \sqrt{3} \right)} + i \pi\right)}{2}$$
-1/2 + sqrt(3)*(pi*i + log(-1 + sqrt(3)))/2 + sqrt(3)*log(3/2 + sqrt(3))/2 - sqrt(3)*(pi*i + log(-3/2 + sqrt(3)))/2 - sqrt(3)*log(1 + sqrt(3))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.