Sr Examen
Integral de (4-x)/(1-4x-5x^2)^(1/2) dx
Solución
Ha introducido
[src]
1 / | | 4 - x | ------------------- dx | ________________ | / 2 | \/ 1 - 4*x - 5*x | / 0
$$\int\limits_{0}^{1} \frac{4 - x}{\sqrt{- 5 x^{2} + \left(1 - 4 x\right)}}\, dx$$
Integral((4 - x)/sqrt(1 - 4*x - 5*x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / | | | | 4 - x | x | 1 | ------------------- dx = C - | ----------------------- dx + 4* | ------------------- dx | ________________ | _____________________ | ________________ | / 2 | \/ -(1 + x)*(-1 + 5*x) | / 2 | \/ 1 - 4*x - 5*x | | \/ 1 - 5*x - 4*x | / | / /
$$\int \frac{4 - x}{\sqrt{- 5 x^{2} + \left(1 - 4 x\right)}}\, dx = C - \int \frac{x}{\sqrt{- \left(x + 1\right) \left(5 x - 1\right)}}\, dx + 4 \int \frac{1}{\sqrt{- 5 x^{2} - 4 x + 1}}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| -4 | x
- | --------------------- dx - | --------------------- dx
| _______ _________ | _______ _________
| \/ 1 + x *\/ 1 - 5*x | \/ 1 + x *\/ 1 - 5*x
| |
/ /
0 0
$$- \int\limits_{0}^{1} \left(- \frac{4}{\sqrt{1 - 5 x} \sqrt{x + 1}}\right)\, dx - \int\limits_{0}^{1} \frac{x}{\sqrt{1 - 5 x} \sqrt{x + 1}}\, dx$$
=
=
1 1
/ /
| |
| -4 | x
- | --------------------- dx - | --------------------- dx
| _______ _________ | _______ _________
| \/ 1 + x *\/ 1 - 5*x | \/ 1 + x *\/ 1 - 5*x
| |
/ /
0 0
$$- \int\limits_{0}^{1} \left(- \frac{4}{\sqrt{1 - 5 x} \sqrt{x + 1}}\right)\, dx - \int\limits_{0}^{1} \frac{x}{\sqrt{1 - 5 x} \sqrt{x + 1}}\, dx$$
-Integral(-4/(sqrt(1 + x)*sqrt(1 - 5*x)), (x, 0, 1)) - Integral(x/(sqrt(1 + x)*sqrt(1 - 5*x)), (x, 0, 1))
Respuesta numérica
[src]
(1.33571362283403 - 2.32109051917494j)
(1.33571362283403 - 2.32109051917494j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.