Sr Examen
Integral de 1/(2+(sqrt(x)/(3+x))) dx
Solución
Ha introducido
[src]
6 / | | 1 | --------- dx | ___ | \/ x | 2 + ----- | 3 + x | / 1
$$\int\limits_{1}^{6} \frac{1}{\frac{\sqrt{x}}{x + 3} + 2}\, dx$$
Integral(1/(2 + sqrt(x)/(3 + x)), (x, 1, 6))
Respuesta (Indefinida)
[src]
/ ____ /1 ___\\
|4*\/ 47 *|- + \/ x ||
/ ____ | \4 /|
| ___ / ___ \ 23*\/ 47 *atan|--------------------|
| 1 x \/ x log\6 + \/ x + 2*x/ \ 47 /
| --------- dx = C + - - ----- + -------------------- + ------------------------------------
| ___ 2 2 8 188
| \/ x
| 2 + -----
| 3 + x
|
/
$$\int \frac{1}{\frac{\sqrt{x}}{x + 3} + 2}\, dx = C - \frac{\sqrt{x}}{2} + \frac{x}{2} + \frac{\log{\left(\sqrt{x} + 2 x + 6 \right)}}{8} + \frac{23 \sqrt{47} \operatorname{atan}{\left(\frac{4 \sqrt{47} \left(\sqrt{x} + \frac{1}{4}\right)}{47} \right)}}{188}$$
Gráfica
Respuesta
[src]
/ ____\ / ____ _____\
____ |5*\/ 47 | ____ |\/ 47 4*\/ 282 |
___ / ___\ 23*\/ 47 *atan|--------| 23*\/ 47 *atan|------ + ---------|
\/ 6 log(72) log\144 + 8*\/ 6 / \ 47 / \ 47 47 /
3 - ----- - ------- + ------------------ - ------------------------ + ----------------------------------
2 8 8 188 188
$$- \frac{\sqrt{6}}{2} - \frac{\log{\left(72 \right)}}{8} - \frac{23 \sqrt{47} \operatorname{atan}{\left(\frac{5 \sqrt{47}}{47} \right)}}{188} + \frac{\log{\left(8 \sqrt{6} + 144 \right)}}{8} + \frac{23 \sqrt{47} \operatorname{atan}{\left(\frac{\sqrt{47}}{47} + \frac{4 \sqrt{282}}{47} \right)}}{188} + 3$$
=
=
/ ____\ / ____ _____\
____ |5*\/ 47 | ____ |\/ 47 4*\/ 282 |
___ / ___\ 23*\/ 47 *atan|--------| 23*\/ 47 *atan|------ + ---------|
\/ 6 log(72) log\144 + 8*\/ 6 / \ 47 / \ 47 47 /
3 - ----- - ------- + ------------------ - ------------------------ + ----------------------------------
2 8 8 188 188
$$- \frac{\sqrt{6}}{2} - \frac{\log{\left(72 \right)}}{8} - \frac{23 \sqrt{47} \operatorname{atan}{\left(\frac{5 \sqrt{47}}{47} \right)}}{188} + \frac{\log{\left(8 \sqrt{6} + 144 \right)}}{8} + \frac{23 \sqrt{47} \operatorname{atan}{\left(\frac{\sqrt{47}}{47} + \frac{4 \sqrt{282}}{47} \right)}}{188} + 3$$
3 - sqrt(6)/2 - log(72)/8 + log(144 + 8*sqrt(6))/8 - 23*sqrt(47)*atan(5*sqrt(47)/47)/188 + 23*sqrt(47)*atan(sqrt(47)/47 + 4*sqrt(282)/47)/188
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.