Sr Examen
Integral de dx/(x+2+(x+1)^1/2) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------- dx | _______ | x + 2 + \/ x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\sqrt{x + 1} + \left(x + 2\right)}\, dx$$
Integral(1/(x + 2 + sqrt(x + 1)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ /1 _______\\
|2*\/ 3 *|- + \/ x + 1 ||
/ ___ | \2 /|
| 2*\/ 3 *atan|-----------------------|
| 1 \ 3 / / _______\
| ----------------- dx = C - ------------------------------------- + log\2 + x + \/ x + 1 /
| _______ 3
| x + 2 + \/ x + 1
|
/
$$\int \frac{1}{\sqrt{x + 1} + \left(x + 2\right)}\, dx = C + \log{\left(x + \sqrt{x + 1} + 2 \right)} - \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\sqrt{x + 1} + \frac{1}{2}\right)}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ___ /1 ___\\
|2*\/ 3 *|- + \/ 2 ||
___ | \2 /|
2*\/ 3 *atan|-------------------| ___
\ 3 / 2*pi*\/ 3 / ___\
-log(3) - --------------------------------- + ---------- + log\3 + \/ 2 /
3 9
$$- \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\frac{1}{2} + \sqrt{2}\right)}{3} \right)}}{3} - \log{\left(3 \right)} + \frac{2 \sqrt{3} \pi}{9} + \log{\left(\sqrt{2} + 3 \right)}$$
=
=
/ ___ /1 ___\\
|2*\/ 3 *|- + \/ 2 ||
___ | \2 /|
2*\/ 3 *atan|-------------------| ___
\ 3 / 2*pi*\/ 3 / ___\
-log(3) - --------------------------------- + ---------- + log\3 + \/ 2 /
3 9
$$- \frac{2 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(\frac{1}{2} + \sqrt{2}\right)}{3} \right)}}{3} - \log{\left(3 \right)} + \frac{2 \sqrt{3} \pi}{9} + \log{\left(\sqrt{2} + 3 \right)}$$
-log(3) - 2*sqrt(3)*atan(2*sqrt(3)*(1/2 + sqrt(2))/3)/3 + 2*pi*sqrt(3)/9 + log(3 + sqrt(2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.