Sr Examen
Integral de (3*x^3-x^2+2*x-4)/sqrt(x^2-3*x+2) dx
Solución
Ha introducido
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1 / | | 3 2 | 3*x - x + 2*x - 4 | ------------------- dx | ______________ | / 2 | \/ x - 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{\left(2 x + \left(3 x^{3} - x^{2}\right)\right) - 4}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx$$
Integral((3*x^3 - x^2 + 2*x - 4)/sqrt(x^2 - 3*x + 2), (x, 0, 1))
Respuesta (Indefinida)
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/ / / | | / / | | 3 2 | 2 | | | 3 | 3*x - x + 2*x - 4 | x | 1 | x | x | ------------------- dx = C - | --------------------- dx - 4* | ----------------- dx + 2* | --------------------- dx + 3* | --------------------- dx | ______________ | ___________________ | ______________ | ___________________ | ___________________ | / 2 | \/ (-1 + x)*(-2 + x) | / 2 | \/ (-1 + x)*(-2 + x) | \/ (-1 + x)*(-2 + x) | \/ x - 3*x + 2 | | \/ x - 3*x + 2 | | | / | / / / /
$$\int \frac{\left(2 x + \left(3 x^{3} - x^{2}\right)\right) - 4}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx = C + 2 \int \frac{x}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx - \int \frac{x^{2}}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx + 3 \int \frac{x^{3}}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx - 4 \int \frac{1}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.