Sr Examen
Integral de sqrt(x)/(3*x-sqrt^3(x^2)) dx
Solución
Ha introducido
[src]
1 / | | ___ | \/ x | -------------- dx | 3 | ____ | / 2 | 3*x - \/ x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{x}}{3 x - \left(\sqrt{x^{2}}\right)^{3}}\, dx$$
Integral(sqrt(x)/(3*x - (sqrt(x^2))^3), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 3/4 ___\ | 4 ___ |3 *\/ x | | ___ 4 ___ / ___ 4 ___\ \/ 3 *atan|----------| 4 ___ /4 ___ ___\ | \/ x \/ 3 *log\\/ x - \/ 3 / \ 3 / \/ 3 *log\\/ 3 + \/ x / | -------------- dx = C - ------------------------ + ---------------------- + ------------------------ | 3 6 3 6 | ____ | / 2 | 3*x - \/ x | /
$$\int \frac{\sqrt{x}}{3 x - \left(\sqrt{x^{2}}\right)^{3}}\, dx = C - \frac{\sqrt[4]{3} \log{\left(\sqrt{x} - \sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \log{\left(\sqrt{x} + \sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \operatorname{atan}{\left(\frac{3^{\frac{3}{4}} \sqrt{x}}{3} \right)}}{3}$$
Respuesta
[src]
/ 3/4\
4 ___ |3 |
4 ___ / / 4 ___\\ 4 ___ /4 ___\ \/ 3 *atan|----| 4 ___ / /4 ___\\ 4 ___ / 4 ___\
\/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 / \ 3 / \/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 /
- ------------------------------ - ---------------- + ---------------- + ------------------------- + --------------------
6 6 3 6 6
$$- \frac{\sqrt[4]{3} \log{\left(\sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \log{\left(1 + \sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \operatorname{atan}{\left(\frac{3^{\frac{3}{4}}}{3} \right)}}{3} - \frac{\sqrt[4]{3} \left(\log{\left(-1 + \sqrt[4]{3} \right)} + i \pi\right)}{6} + \frac{\sqrt[4]{3} \left(\log{\left(\sqrt[4]{3} \right)} + i \pi\right)}{6}$$
=
=
/ 3/4\
4 ___ |3 |
4 ___ / / 4 ___\\ 4 ___ /4 ___\ \/ 3 *atan|----| 4 ___ / /4 ___\\ 4 ___ / 4 ___\
\/ 3 *\pi*I + log\-1 + \/ 3 // \/ 3 *log\\/ 3 / \ 3 / \/ 3 *\pi*I + log\\/ 3 // \/ 3 *log\1 + \/ 3 /
- ------------------------------ - ---------------- + ---------------- + ------------------------- + --------------------
6 6 3 6 6
$$- \frac{\sqrt[4]{3} \log{\left(\sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \log{\left(1 + \sqrt[4]{3} \right)}}{6} + \frac{\sqrt[4]{3} \operatorname{atan}{\left(\frac{3^{\frac{3}{4}}}{3} \right)}}{3} - \frac{\sqrt[4]{3} \left(\log{\left(-1 + \sqrt[4]{3} \right)} + i \pi\right)}{6} + \frac{\sqrt[4]{3} \left(\log{\left(\sqrt[4]{3} \right)} + i \pi\right)}{6}$$
-3^(1/4)*(pi*i + log(-1 + 3^(1/4)))/6 - 3^(1/4)*log(3^(1/4))/6 + 3^(1/4)*atan(3^(3/4)/3)/3 + 3^(1/4)*(pi*i + log(3^(1/4)))/6 + 3^(1/4)*log(1 + 3^(1/4))/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.