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