Sr Examen
Integral de sqrt(x+2)/(3*x+1) dx
Solución
Ha introducido
[src]
1 / | | _______ | \/ x + 2 | --------- dx | 3*x + 1 | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x + 2}}{3 x + 1}\, dx$$
Integral(sqrt(x + 2)/(3*x + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ _______\ \
|| ____ |\/ 15 *\/ 2 + x | |
||-\/ 15 *acoth|----------------| |
|| \ 5 / |
||-------------------------------- for 2 + x > 5/3|
|| 15 |
10*|< |
|| / ____ _______\ |
|| ____ |\/ 15 *\/ 2 + x | |
/ ||-\/ 15 *atanh|----------------| |
| || \ 5 / |
| _______ _______ ||-------------------------------- for 2 + x < 5/3|
| \/ x + 2 2*\/ 2 + x \\ 15 /
| --------- dx = C + ----------- + -------------------------------------------------------
| 3*x + 1 3 3
|
/
$$\int \frac{\sqrt{x + 2}}{3 x + 1}\, dx = C + \frac{2 \sqrt{x + 2}}{3} + \frac{10 \left(\begin{cases} - \frac{\sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{15} \sqrt{x + 2}}{5} \right)}}{15} & \text{for}\: x + 2 > \frac{5}{3} \\- \frac{\sqrt{15} \operatorname{atanh}{\left(\frac{\sqrt{15} \sqrt{x + 2}}{5} \right)}}{15} & \text{for}\: x + 2 < \frac{5}{3} \end{cases}\right)}{3}$$
Gráfica
Respuesta
[src]
/ ___\ / ____\
____ |3*\/ 5 | ____ |\/ 30 |
___ ___ 2*\/ 15 *acoth|-------| 2*\/ 15 *acoth|------|
2*\/ 2 2*\/ 3 \ 5 / \ 5 /
- ------- + ------- - ----------------------- + ----------------------
3 3 9 9
$$- \frac{2 \sqrt{2}}{3} - \frac{2 \sqrt{15} \operatorname{acoth}{\left(\frac{3 \sqrt{5}}{5} \right)}}{9} + \frac{2 \sqrt{3}}{3} + \frac{2 \sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{30}}{5} \right)}}{9}$$
=
=
/ ___\ / ____\
____ |3*\/ 5 | ____ |\/ 30 |
___ ___ 2*\/ 15 *acoth|-------| 2*\/ 15 *acoth|------|
2*\/ 2 2*\/ 3 \ 5 / \ 5 /
- ------- + ------- - ----------------------- + ----------------------
3 3 9 9
$$- \frac{2 \sqrt{2}}{3} - \frac{2 \sqrt{15} \operatorname{acoth}{\left(\frac{3 \sqrt{5}}{5} \right)}}{9} + \frac{2 \sqrt{3}}{3} + \frac{2 \sqrt{15} \operatorname{acoth}{\left(\frac{\sqrt{30}}{5} \right)}}{9}$$
-2*sqrt(2)/3 + 2*sqrt(3)/3 - 2*sqrt(15)*acoth(3*sqrt(5)/5)/9 + 2*sqrt(15)*acoth(sqrt(30)/5)/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.