Sr Examen
Integral de cbrt(1+x^(1/4)) dx
Solución
Ha introducido
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1 / | | ___________ | 3 / 4 ___ | \/ 1 + \/ x dx | / 0
$$\int\limits_{0}^{1} \sqrt[3]{\sqrt[4]{x} + 1}\, dx$$
Integral((1 + x^(1/4))^(1/3), (x, 0, 1))
Respuesta (Indefinida)
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/ | ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ | ___________ 4 11/2 17/4 21/4 5 9/2 19/4 19/4 3 / 4 ___ 9/2 3 / 4 ___ 5 3 / 4 ___ 17/4 3 / 4 ___ 4 3 / 4 ___ 13/2 3 / 4 ___ 21/4 3 / 4 ___ 25/4 3 / 4 ___ 6 3 / 4 ___ 11/2 3 / 4 ___ 23/4 3 / 4 ___ | 3 / 4 ___ 243*x 243*x 1458*x 1458*x 3645*x 3645*x 4860*x 3927*x *\/ 1 + \/ x 3213*x *\/ 1 + \/ x 2163*x *\/ 1 + \/ x 1377*x *\/ 1 + \/ x 243*x *\/ 1 + \/ x 420*x *\/ 1 + \/ x 1827*x *\/ 1 + \/ x 2562*x *\/ 1 + \/ x 6498*x *\/ 1 + \/ x 6573*x *\/ 1 + \/ x 8787*x *\/ 1 + \/ x | \/ 1 + \/ x dx = C + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- - ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- + ------------------------------------------------------------------------------- | 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 4 11/2 17/4 21/4 5 9/2 19/4 / 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x 455*x + 455*x + 2730*x + 2730*x + 6825*x + 6825*x + 9100*x
$$\int \sqrt[3]{\sqrt[4]{x} + 1}\, dx = C + \frac{2562 x^{\frac{25}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{8787 x^{\frac{23}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{1827 x^{\frac{21}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{1458 x^{\frac{21}{4}}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} - \frac{3927 x^{\frac{19}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{4860 x^{\frac{19}{4}}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} - \frac{1377 x^{\frac{17}{4}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{1458 x^{\frac{17}{4}}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{420 x^{\frac{13}{2}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{6573 x^{\frac{11}{2}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{243 x^{\frac{11}{2}}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} - \frac{3213 x^{\frac{9}{2}} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{3645 x^{\frac{9}{2}}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{6498 x^{6} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} - \frac{2163 x^{5} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{3645 x^{5}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} - \frac{243 x^{4} \sqrt[3]{\sqrt[4]{x} + 1}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}} + \frac{243 x^{4}}{2730 x^{\frac{21}{4}} + 9100 x^{\frac{19}{4}} + 2730 x^{\frac{17}{4}} + 455 x^{\frac{11}{2}} + 6825 x^{\frac{9}{2}} + 6825 x^{5} + 455 x^{4}}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.