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