Sr Examen
Integral de 1/((x+1)(sqrt(x+4))) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------- dx | _______ | (x + 1)*\/ x + 4 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(x + 1\right) \sqrt{x + 4}}\, dx$$
Integral(1/((x + 1)*sqrt(x + 4)), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ___ _______\ \
|| ___ |\/ 3 *\/ 4 + x | |
||-\/ 3 *acoth|---------------| |
/ || \ 3 / |
| ||------------------------------ for 4 + x > 3|
| 1 || 3 |
| ----------------- dx = C + 2*|< |
| _______ || / ___ _______\ |
| (x + 1)*\/ x + 4 || ___ |\/ 3 *\/ 4 + x | |
| ||-\/ 3 *atanh|---------------| |
/ || \ 3 / |
||------------------------------ for 4 + x < 3|
\\ 3 /
$$\int \frac{1}{\left(x + 1\right) \sqrt{x + 4}}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{3} \operatorname{acoth}{\left(\frac{\sqrt{3} \sqrt{x + 4}}{3} \right)}}{3} & \text{for}\: x + 4 > 3 \\- \frac{\sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3} \sqrt{x + 4}}{3} \right)}}{3} & \text{for}\: x + 4 < 3 \end{cases}\right)$$
Gráfica
Respuesta
[src]
/ ____\ / ___\
___ |\/ 15 | ___ |\/ 3 |
2*\/ 3 *atanh|------| 2*\/ 3 *atanh|-----|
\ 5 / \ 2 /
- --------------------- + --------------------
3 3
$$- \frac{2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{15}}{5} \right)}}{3} + \frac{2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3}}{2} \right)}}{3}$$
=
=
/ ____\ / ___\
___ |\/ 15 | ___ |\/ 3 |
2*\/ 3 *atanh|------| 2*\/ 3 *atanh|-----|
\ 5 / \ 2 /
- --------------------- + --------------------
3 3
$$- \frac{2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{15}}{5} \right)}}{3} + \frac{2 \sqrt{3} \operatorname{atanh}{\left(\frac{\sqrt{3}}{2} \right)}}{3}$$
-2*sqrt(3)*atanh(sqrt(15)/5)/3 + 2*sqrt(3)*atanh(sqrt(3)/2)/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.