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