Sr Examen
Integral de x+1/x2/(2+x)/(x-2) dx
Solución
Ha introducido
[src]
___ \/ 3 / | | / / 1 \\ | | |----------|| | | \x2*(2 + x)/| | |x + ------------| dx | \ x - 2 / | / ___ \/ 3 ----- 3
$$\int\limits_{\frac{\sqrt{3}}{3}}^{\sqrt{3}} \left(x + \frac{\frac{1}{x_{2}} \frac{1}{x + 2}}{x - 2}\right)\, dx$$
Integral(x + (1/(x2*(2 + x)))/(x - 2), (x, sqrt(3)/3, sqrt(3)))
Respuesta (Indefinida)
[src]
/ | | / / 1 \\ | | |----------|| 2 | | \x2*(2 + x)/| x log(2 + x) log(-2 + x) | |x + ------------| dx = C + -- - ---------- + ----------- | \ x - 2 / 2 4*x2 4*x2 | /
$$\int \left(x + \frac{\frac{1}{x_{2}} \frac{1}{x + 2}}{x - 2}\right)\, dx = C + \frac{x^{2}}{2} + \frac{\log{\left(x - 2 \right)}}{4 x_{2}} - \frac{\log{\left(x + 2 \right)}}{4 x_{2}}$$
Respuesta
[src]
/ ___\ / ___\
| \/ 3 | | \/ 3 |
/ ___\ / ___\ log|2 + -----| log|2 - -----|
log\2 + \/ 3 / log\2 - \/ 3 / pi*I \ 3 / \ 3 / pi*I
- -------------- + -------------- + ---- - -------------- + -------------- + ----
4 4 4 4 4 4 4
- + ---------------------------------------- - ----------------------------------------
3 x2 x2
$$\frac{4}{3} - \frac{- \frac{\log{\left(\frac{\sqrt{3}}{3} + 2 \right)}}{4} + \frac{\log{\left(2 - \frac{\sqrt{3}}{3} \right)}}{4} + \frac{i \pi}{4}}{x_{2}} + \frac{- \frac{\log{\left(\sqrt{3} + 2 \right)}}{4} + \frac{\log{\left(2 - \sqrt{3} \right)}}{4} + \frac{i \pi}{4}}{x_{2}}$$
=
=
/ ___\ / ___\
| \/ 3 | | \/ 3 |
/ ___\ / ___\ log|2 + -----| log|2 - -----|
log\2 + \/ 3 / log\2 - \/ 3 / pi*I \ 3 / \ 3 / pi*I
- -------------- + -------------- + ---- - -------------- + -------------- + ----
4 4 4 4 4 4 4
- + ---------------------------------------- - ----------------------------------------
3 x2 x2
$$\frac{4}{3} - \frac{- \frac{\log{\left(\frac{\sqrt{3}}{3} + 2 \right)}}{4} + \frac{\log{\left(2 - \frac{\sqrt{3}}{3} \right)}}{4} + \frac{i \pi}{4}}{x_{2}} + \frac{- \frac{\log{\left(\sqrt{3} + 2 \right)}}{4} + \frac{\log{\left(2 - \sqrt{3} \right)}}{4} + \frac{i \pi}{4}}{x_{2}}$$
4/3 + (-log(2 + sqrt(3))/4 + log(2 - sqrt(3))/4 + pi*i/4)/x2 - (-log(2 + sqrt(3)/3)/4 + log(2 - sqrt(3)/3)/4 + pi*i/4)/x2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.