Sr Examen
Integral de (5-2x)/((-x^2)+6x-5)^(1/2) dx
Solución
Ha introducido
[src]
4 / | | 5 - 2*x | ------------------- dx | ________________ | / 2 | \/ - x + 6*x - 5 | / 3
$$\int\limits_{3}^{4} \frac{5 - 2 x}{\sqrt{\left(- x^{2} + 6 x\right) - 5}}\, dx$$
Integral((5 - 2*x)/sqrt(-x^2 + 6*x - 5), (x, 3, 4))
Respuesta (Indefinida)
[src]
/ / / | | | | 5 - 2*x | x | 1 | ------------------- dx = C - 2* | ---------------------- dx + 5* | ------------------ dx | ________________ | ____________________ | _______________ | / 2 | \/ -(-1 + x)*(-5 + x) | / 2 | \/ - x + 6*x - 5 | | \/ -5 - x + 6*x | / | / /
$$\int \frac{5 - 2 x}{\sqrt{\left(- x^{2} + 6 x\right) - 5}}\, dx = C - 2 \int \frac{x}{\sqrt{- \left(x - 5\right) \left(x - 1\right)}}\, dx + 5 \int \frac{1}{\sqrt{- x^{2} + 6 x - 5}}\, dx$$
Respuesta
[src]
4 4
/ /
| |
| -5 | 2*x
- | ------------------ dx - | ------------------ dx
| _______________ | _______________
| / 2 | / 2
| \/ -5 - x + 6*x | \/ -5 - x + 6*x
| |
/ /
3 3
$$- \int\limits_{3}^{4} \frac{2 x}{\sqrt{- x^{2} + 6 x - 5}}\, dx - \int\limits_{3}^{4} \left(- \frac{5}{\sqrt{- x^{2} + 6 x - 5}}\right)\, dx$$
=
=
4 4
/ /
| |
| -5 | 2*x
- | ------------------ dx - | ------------------ dx
| _______________ | _______________
| / 2 | / 2
| \/ -5 - x + 6*x | \/ -5 - x + 6*x
| |
/ /
3 3
$$- \int\limits_{3}^{4} \frac{2 x}{\sqrt{- x^{2} + 6 x - 5}}\, dx - \int\limits_{3}^{4} \left(- \frac{5}{\sqrt{- x^{2} + 6 x - 5}}\right)\, dx$$
-Integral(-5/sqrt(-5 - x^2 + 6*x), (x, 3, 4)) - Integral(2*x/sqrt(-5 - x^2 + 6*x), (x, 3, 4))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.