Sr Examen
Integral de (x)/(sqrt(2+x^(2/3))) dx
Solución
Ha introducido
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1 / | | x | ------------- dx | __________ | / 2/3 | \/ 2 + x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x^{\frac{2}{3}} + 2}}\, dx$$
Integral(x/sqrt(2 + x^(2/3)), (x, 0, 1))
Respuesta (Indefinida)
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$$\int \frac{x}{\sqrt{x^{\frac{2}{3}} + 2}}\, dx = C + \frac{3 \sqrt{2} x^{\frac{28}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{10 \sqrt{2} x^{\frac{26}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{120 \sqrt{2} x^{\frac{22}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{384 x^{\frac{22}{3}}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{320 \sqrt{2} x^{\frac{20}{3}} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{768 x^{\frac{20}{3}}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{20 \sqrt{2} x^{8} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{64 x^{8}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} + \frac{256 \sqrt{2} x^{6} \sqrt{x^{\frac{2}{3}} + 2}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}} - \frac{512 x^{6}}{30 \sqrt{2} x^{\frac{22}{3}} + 60 \sqrt{2} x^{\frac{20}{3}} + 5 \sqrt{2} x^{8} + 40 \sqrt{2} x^{6}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.