Sr Examen
Integral de (dx)/(x+(√x+6)) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------------- dx | ___ | x + \/ x + 6 | / 0
$$\int\limits_{0}^{1} \frac{1}{x + \left(\sqrt{x} + 6\right)}\, dx$$
Integral(1/(x + sqrt(x) + 6), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ /1 ___\\
|2*\/ 23 *|- + \/ x ||
/ ____ | \2 /|
| 2*\/ 23 *atan|--------------------|
| 1 \ 23 / / ___\
| ------------- dx = C - ----------------------------------- + log\6 + x + \/ x /
| ___ 23
| x + \/ x + 6
|
/
$$\int \frac{1}{x + \left(\sqrt{x} + 6\right)}\, dx = C + \log{\left(\sqrt{x} + x + 6 \right)} - \frac{2 \sqrt{23} \operatorname{atan}{\left(\frac{2 \sqrt{23} \left(\sqrt{x} + \frac{1}{2}\right)}{23} \right)}}{23}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |3*\/ 23 | ____ |\/ 23 |
2*\/ 23 *atan|--------| 2*\/ 23 *atan|------|
\ 23 / \ 23 /
-log(24) - ----------------------- + --------------------- + log(32)
23 23
$$- \log{\left(24 \right)} - \frac{2 \sqrt{23} \operatorname{atan}{\left(\frac{3 \sqrt{23}}{23} \right)}}{23} + \frac{2 \sqrt{23} \operatorname{atan}{\left(\frac{\sqrt{23}}{23} \right)}}{23} + \log{\left(32 \right)}$$
=
=
/ ____\ / ____\
____ |3*\/ 23 | ____ |\/ 23 |
2*\/ 23 *atan|--------| 2*\/ 23 *atan|------|
\ 23 / \ 23 /
-log(24) - ----------------------- + --------------------- + log(32)
23 23
$$- \log{\left(24 \right)} - \frac{2 \sqrt{23} \operatorname{atan}{\left(\frac{3 \sqrt{23}}{23} \right)}}{23} + \frac{2 \sqrt{23} \operatorname{atan}{\left(\frac{\sqrt{23}}{23} \right)}}{23} + \log{\left(32 \right)}$$
-log(24) - 2*sqrt(23)*atan(3*sqrt(23)/23)/23 + 2*sqrt(23)*atan(sqrt(23)/23)/23 + log(32)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.