Sr Examen
Integral de sqrt(x^2+1)/(16-x^4)^(1/3) dx
Solución
Ha introducido
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oo / | | ________ | / 2 | \/ x + 1 | ------------ dx | _________ | 3 / 4 | \/ 16 - x | / 2
$$\int\limits_{2}^{\infty} \frac{\sqrt{x^{2} + 1}}{\sqrt[3]{16 - x^{4}}}\, dx$$
Integral(sqrt(x^2 + 1)/(16 - x^4)^(1/3), (x, 2, oo))
Respuesta (Indefinida)
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/ / | | | ________ | ________ | / 2 | / 2 | \/ x + 1 | \/ 1 + x | ------------ dx = C + | ------------------------------- dx | _________ | ____________________________ | 3 / 4 | 3 / / 2\ | \/ 16 - x | \/ -(-2 + x)*(2 + x)*\4 + x / | | / /
$$\int \frac{\sqrt{x^{2} + 1}}{\sqrt[3]{16 - x^{4}}}\, dx = C + \int \frac{\sqrt{x^{2} + 1}}{\sqrt[3]{- \left(x - 2\right) \left(x + 2\right) \left(x^{2} + 4\right)}}\, dx$$
Gráfica
Respuesta
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oo / | | ________ | / 2 | \/ 1 + x | ------------------------------- dx | ____________________________ | 3 / / 2\ | \/ -(-2 + x)*(2 + x)*\4 + x / | / 2
$$\int\limits_{2}^{\infty} \frac{\sqrt{x^{2} + 1}}{\sqrt[3]{- \left(x - 2\right) \left(x + 2\right) \left(x^{2} + 4\right)}}\, dx$$
=
=
oo / | | ________ | / 2 | \/ 1 + x | ------------------------------- dx | ____________________________ | 3 / / 2\ | \/ -(-2 + x)*(2 + x)*\4 + x / | / 2
$$\int\limits_{2}^{\infty} \frac{\sqrt{x^{2} + 1}}{\sqrt[3]{- \left(x - 2\right) \left(x + 2\right) \left(x^{2} + 4\right)}}\, dx$$
Integral(sqrt(1 + x^2)/(-(-2 + x)*(2 + x)*(4 + x^2))^(1/3), (x, 2, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.