Sr Examen
Integral de x/(1+x^(2/3))^(1/2) dx
Solución
Ha introducido
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1 / | | x | ------------- dx | __________ | / 2/3 | \/ 1 + x | / 0
$$\int\limits_{0}^{1} \frac{x}{\sqrt{x^{\frac{2}{3}} + 1}}\, dx$$
Integral(x/sqrt(1 + x^(2/3)), (x, 0, 1))
Respuesta (Indefinida)
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/ __________ __________ __________ __________ __________ __________ | 20/3 22/3 6 8 28/3 / 2/3 8 / 2/3 26/3 / 2/3 6 / 2/3 22/3 / 2/3 20/3 / 2/3 | x 24*x 24*x 8*x 8*x 3*x *\/ 1 + x 5*x *\/ 1 + x 5*x *\/ 1 + x 8*x *\/ 1 + x 15*x *\/ 1 + x 20*x *\/ 1 + x | ------------- dx = C - --------------------------------- - --------------------------------- - --------------------------------- - --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- + --------------------------------- | __________ 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 6 8 20/3 22/3 | / 2/3 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x 5*x + 5*x + 15*x + 15*x | \/ 1 + x | /
$$\int \frac{x}{\sqrt{x^{\frac{2}{3}} + 1}}\, dx = C + \frac{3 x^{\frac{28}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} + \frac{5 x^{\frac{26}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} + \frac{15 x^{\frac{22}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} - \frac{24 x^{\frac{22}{3}}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} + \frac{20 x^{\frac{20}{3}} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} - \frac{24 x^{\frac{20}{3}}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} + \frac{5 x^{8} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} - \frac{8 x^{8}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} + \frac{8 x^{6} \sqrt{x^{\frac{2}{3}} + 1}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}} - \frac{8 x^{6}}{15 x^{\frac{22}{3}} + 15 x^{\frac{20}{3}} + 5 x^{8} + 5 x^{6}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.