Sr Examen
Integral de 1/(x-(3*x+2)^1/3) dx
Solución
Ha introducido
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1 / | | 1 | --------------- dx | 3 _________ | x - \/ 3*x + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{x - \sqrt[3]{3 x + 2}}\, dx$$
Integral(1/(x - (3*x + 2)^(1/3)), (x, 0, 1))
Respuesta (Indefinida)
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/ | / 3 _________\ / 3 _________\ | 1 1 4*log\-2 + \/ 3*x + 2 / 5*log\1 + \/ 3*x + 2 / | --------------- dx = C + --------------- + ----------------------- + ---------------------- | 3 _________ 3 _________ 3 3 | x - \/ 3*x + 2 1 + \/ 3*x + 2 | /
$$\int \frac{1}{x - \sqrt[3]{3 x + 2}}\, dx = C + \frac{4 \log{\left(\sqrt[3]{3 x + 2} - 2 \right)}}{3} + \frac{5 \log{\left(\sqrt[3]{3 x + 2} + 1 \right)}}{3} + \frac{1}{\sqrt[3]{3 x + 2} + 1}$$
Gráfica
Respuesta
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/ 3 ___\ / 3 ___\ / 3 ___\ / 3 ___\
1 1 5*log\1 + \/ 2 / 4*log\2 - \/ 2 / 4*log\2 - \/ 5 / 5*log\1 + \/ 5 /
--------- - --------- - ---------------- - ---------------- + ---------------- + ----------------
3 ___ 3 ___ 3 3 3 3
1 + \/ 5 1 + \/ 2
$$\frac{4 \log{\left(2 - \sqrt[3]{5} \right)}}{3} - \frac{5 \log{\left(1 + \sqrt[3]{2} \right)}}{3} - \frac{1}{1 + \sqrt[3]{2}} + \frac{1}{1 + \sqrt[3]{5}} - \frac{4 \log{\left(2 - \sqrt[3]{2} \right)}}{3} + \frac{5 \log{\left(1 + \sqrt[3]{5} \right)}}{3}$$
=
=
/ 3 ___\ / 3 ___\ / 3 ___\ / 3 ___\
1 1 5*log\1 + \/ 2 / 4*log\2 - \/ 2 / 4*log\2 - \/ 5 / 5*log\1 + \/ 5 /
--------- - --------- - ---------------- - ---------------- + ---------------- + ----------------
3 ___ 3 ___ 3 3 3 3
1 + \/ 5 1 + \/ 2
$$\frac{4 \log{\left(2 - \sqrt[3]{5} \right)}}{3} - \frac{5 \log{\left(1 + \sqrt[3]{2} \right)}}{3} - \frac{1}{1 + \sqrt[3]{2}} + \frac{1}{1 + \sqrt[3]{5}} - \frac{4 \log{\left(2 - \sqrt[3]{2} \right)}}{3} + \frac{5 \log{\left(1 + \sqrt[3]{5} \right)}}{3}$$
1/(1 + 5^(1/3)) - 1/(1 + 2^(1/3)) - 5*log(1 + 2^(1/3))/3 - 4*log(2 - 2^(1/3))/3 + 4*log(2 - 5^(1/3))/3 + 5*log(1 + 5^(1/3))/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.