Sr Examen
Integral de ((3*2+x^2+(4x-16)dx))/((x^2-3x+2)^(1/2)) dx
Solución
Ha introducido
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1 / | | 2 | 6 + x + 4*x - 16 | ----------------- dx | ______________ | / 2 | \/ x - 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{\left(4 x - 16\right) + \left(x^{2} + 6\right)}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx$$
Integral((6 + x^2 + 4*x - 16)/sqrt(x^2 - 3*x + 2), (x, 0, 1))
Respuesta (Indefinida)
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/ / | / / | | 2 | | | 2 | 6 + x + 4*x - 16 | 1 | x | x | ----------------- dx = C - 10* | ----------------- dx + 4* | --------------------- dx + | --------------------- dx | ______________ | ______________ | ___________________ | ___________________ | / 2 | / 2 | \/ (-1 + x)*(-2 + x) | \/ (-1 + x)*(-2 + x) | \/ x - 3*x + 2 | \/ x - 3*x + 2 | | | | / / / /
$$\int \frac{\left(4 x - 16\right) + \left(x^{2} + 6\right)}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx = C + 4 \int \frac{x}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx + \int \frac{x^{2}}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx - 10 \int \frac{1}{\sqrt{\left(x^{2} - 3 x\right) + 2}}\, dx$$
Respuesta
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1 / | | 2 | -10 + x + 4*x | --------------------- dx | ___________________ | \/ (-1 + x)*(-2 + x) | / 0
$$\int\limits_{0}^{1} \frac{x^{2} + 4 x - 10}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx$$
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1 / | | 2 | -10 + x + 4*x | --------------------- dx | ___________________ | \/ (-1 + x)*(-2 + x) | / 0
$$\int\limits_{0}^{1} \frac{x^{2} + 4 x - 10}{\sqrt{\left(x - 2\right) \left(x - 1\right)}}\, dx$$
Integral((-10 + x^2 + 4*x)/sqrt((-1 + x)*(-2 + x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.