Sr Examen
Integral de (x+8*cbrt(x^2)+17*cbrt(x)+1)/(x+3*cbrt(x^2)) dx
Solución
Ha introducido
[src]
64 / | | ____ | 3 / 2 3 ___ | x + 8*\/ x + 17*\/ x + 1 | ---------------------------- dx | ____ | 3 / 2 | x + 3*\/ x | / 1
$$\int\limits_{1}^{64} \frac{\left(17 \sqrt[3]{x} + \left(x + 8 \sqrt[3]{x^{2}}\right)\right) + 1}{x + 3 \sqrt[3]{x^{2}}}\, dx$$
Integral((x + 8*(x^2)^(1/3) + 17*x^(1/3) + 1)/(x + 3*(x^2)^(1/3)), (x, 1, 64))
Respuesta (Indefinida)
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/ / | | / | ____ | ____ | / | 3 / 2 3 ___ / ____\ | 3 / 2 | 3 ___ | | x + 8*\/ x + 17*\/ x + 1 | 3 / 2 | | \/ x | \/ x | x | ---------------------------- dx = C - 2*log(x) + 3*log\x + 3*\/ x / + 8* | ------------- dx + 17* | ------------- dx + | ------------- dx | ____ | ____ | ____ | ____ | 3 / 2 | 3 / 2 | 3 / 2 | 3 / 2 | x + 3*\/ x | x + 3*\/ x | x + 3*\/ x | x + 3*\/ x | | | | / / / /
$$\int \frac{\left(17 \sqrt[3]{x} + \left(x + 8 \sqrt[3]{x^{2}}\right)\right) + 1}{x + 3 \sqrt[3]{x^{2}}}\, dx = C - 2 \log{\left(x \right)} + 3 \log{\left(x + 3 \sqrt[3]{x^{2}} \right)} + 17 \int \frac{\sqrt[3]{x}}{x + 3 \sqrt[3]{x^{2}}}\, dx + \int \frac{x}{x + 3 \sqrt[3]{x^{2}}}\, dx + 8 \int \frac{\sqrt[3]{x^{2}}}{x + 3 \sqrt[3]{x^{2}}}\, dx$$
Respuesta
[src]
387/2 - 15*log(7) + 15*log(4)
$$- 15 \log{\left(7 \right)} + 15 \log{\left(4 \right)} + \frac{387}{2}$$
=
=
387/2 - 15*log(7) + 15*log(4)
$$- 15 \log{\left(7 \right)} + 15 \log{\left(4 \right)} + \frac{387}{2}$$
387/2 - 15*log(7) + 15*log(4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.