Sr Examen
Integral de (2x+4)/(sqrt(8-2x-x^2)) dx
Solución
Ha introducido
[src]
1 / | | 2*x + 4 | ----------------- dx | ______________ | / 2 | \/ 8 - 2*x - x | / 0
$$\int\limits_{0}^{1} \frac{2 x + 4}{\sqrt{- x^{2} + \left(8 - 2 x\right)}}\, dx$$
Integral((2*x + 4)/sqrt(8 - 2*x - x^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / / | | | | 2*x + 4 | x | 1 | ----------------- dx = C + 2* | --------------------- dx + 4* | ----------------- dx | ______________ | ___________________ | ______________ | / 2 | \/ -(-2 + x)*(4 + x) | / 2 | \/ 8 - 2*x - x | | \/ 8 - 2*x - x | / | / /
$$\int \frac{2 x + 4}{\sqrt{- x^{2} + \left(8 - 2 x\right)}}\, dx = C + 2 \int \frac{x}{\sqrt{- \left(x - 2\right) \left(x + 4\right)}}\, dx + 4 \int \frac{1}{\sqrt{- x^{2} + \left(8 - 2 x\right)}}\, dx$$
Respuesta
[src]
1 1
/ /
| |
| 2 | x
2* | ------------------- dx + 2* | ------------------- dx
| _______ _______ | _______ _______
| \/ 2 - x *\/ 4 + x | \/ 2 - x *\/ 4 + x
| |
/ /
0 0
$$2 \int\limits_{0}^{1} \frac{x}{\sqrt{2 - x} \sqrt{x + 4}}\, dx + 2 \int\limits_{0}^{1} \frac{2}{\sqrt{2 - x} \sqrt{x + 4}}\, dx$$
=
=
1 1
/ /
| |
| 2 | x
2* | ------------------- dx + 2* | ------------------- dx
| _______ _______ | _______ _______
| \/ 2 - x *\/ 4 + x | \/ 2 - x *\/ 4 + x
| |
/ /
0 0
$$2 \int\limits_{0}^{1} \frac{x}{\sqrt{2 - x} \sqrt{x + 4}}\, dx + 2 \int\limits_{0}^{1} \frac{2}{\sqrt{2 - x} \sqrt{x + 4}}\, dx$$
2*Integral(2/(sqrt(2 - x)*sqrt(4 + x)), (x, 0, 1)) + 2*Integral(x/(sqrt(2 - x)*sqrt(4 + x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.