Sr Examen
Integral de (arctanx)/(9+x^2)^1.5 dx
Solución
Ha introducido
[src]
1 / | | atan(x) | ----------- dx | 3/2 | / 2\ | \9 + x / | / 0
$$\int\limits_{0}^{1} \frac{\operatorname{atan}{\left(x \right)}}{\left(x^{2} + 9\right)^{\frac{3}{2}}}\, dx$$
Integral(atan(x)/(9 + x^2)^(3/2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ___ \
| ___ | 2*\/ 2 |
|-\/ 2 *acoth|-----------|
| | ________|
| | / 2 |
| \\/ 9 + x / 1
|-------------------------- for ------ > 1/8
| 4 2
| 9 + x
<
| / ___ \
| ___ | 2*\/ 2 |
|-\/ 2 *atanh|-----------|
| | ________|
| | / 2 |
| \\/ 9 + x / 1
/ |-------------------------- for ------ < 1/8
| | 4 2
| atan(x) \ 9 + x x*atan(x)
| ----------- dx = C - --------------------------------------------- + -------------
| 3/2 9 ________
| / 2\ / 2
| \9 + x / 9*\/ 9 + x
|
/
$$\int \frac{\operatorname{atan}{\left(x \right)}}{\left(x^{2} + 9\right)^{\frac{3}{2}}}\, dx = C + \frac{x \operatorname{atan}{\left(x \right)}}{9 \sqrt{x^{2} + 9}} - \frac{\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{2 \sqrt{2}}{\sqrt{x^{2} + 9}} \right)}}{4} & \text{for}\: \frac{1}{x^{2} + 9} > \frac{1}{8} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{2 \sqrt{2}}{\sqrt{x^{2} + 9}} \right)}}{4} & \text{for}\: \frac{1}{x^{2} + 9} < \frac{1}{8} \end{cases}}{9}$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.