Sr Examen
Integral de -x^2/(9*x+18)^(2/3)+((2x^3+2x^2)/(3*(3x^2+6x+12)^(2/3))) dx
Solución
Ha introducido
[src]
22 / | | / 2 3 2 \ | | -x 2*x + 2*x | | |------------- + ----------------------| dx | | 2/3 2/3| | |(9*x + 18) / 2 \ | | \ 3*\3*x + 6*x + 12/ / | / -2
$$\int\limits_{-2}^{22} \left(\frac{\left(-1\right) x^{2}}{\left(9 x + 18\right)^{\frac{2}{3}}} + \frac{2 x^{3} + 2 x^{2}}{3 \left(\left(3 x^{2} + 6 x\right) + 12\right)^{\frac{2}{3}}}\right)\, dx$$
Integral((-x^2)/(9*x + 18)^(2/3) + (2*x^3 + 2*x^2)/((3*(3*x^2 + 6*x + 12)^(2/3))), (x, -2, 22))
Respuesta (Indefinida)
[src]
/ /
| |
| 2 | 3
3 ___ | x 3 ___ | x
2*\/ 3 * | ----------------- dx 2*\/ 3 * | ----------------- dx
| 2/3 | 2/3
/ / 3 _______ 3 _______ 2 3 _______\ | / 2 \ | / 2 \
| 2/3 |54*\/ 2 + x 9*x*\/ 2 + x 3*x *\/ 2 + x | | \4 + x + 2*x/ | \4 + x + 2*x/
| / 2 3 2 \ 3 *|------------ - ------------- + --------------| | |
| | -x 2*x + 2*x | \ 7 7 7 / / /
| |------------- + ----------------------| dx = C - ---------------------------------------------------- + ------------------------------- + -------------------------------
| | 2/3 2/3| 9 9 9
| |(9*x + 18) / 2 \ |
| \ 3*\3*x + 6*x + 12/ /
|
/
$$\int \left(\frac{\left(-1\right) x^{2}}{\left(9 x + 18\right)^{\frac{2}{3}}} + \frac{2 x^{3} + 2 x^{2}}{3 \left(\left(3 x^{2} + 6 x\right) + 12\right)^{\frac{2}{3}}}\right)\, dx = C - \frac{3^{\frac{2}{3}} \left(\frac{3 x^{2} \sqrt[3]{x + 2}}{7} - \frac{9 x \sqrt[3]{x + 2}}{7} + \frac{54 \sqrt[3]{x + 2}}{7}\right)}{9} + \frac{2 \sqrt[3]{3} \int \frac{x^{2}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx}{9} + \frac{2 \sqrt[3]{3} \int \frac{x^{3}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx}{9}$$
Respuesta
[src]
/ 22 22 22 \
| / / / |
| | | | |
| | 2 | 3 | 3 ___ 2 |
3 ___ | | 2*x | 2*x | -\/ 3 *x |
\/ 3 *| | ----------------- dx + | ----------------- dx + | ---------- dx|
| | 2/3 | 2/3 | 2/3 |
| | / 2 \ | / 2 \ | (2 + x) |
| | \4 + x + 2*x/ | \4 + x + 2*x/ | |
| | | / |
|/ / -2 |
\-2 -2 /
-------------------------------------------------------------------------------
9
$$\frac{\sqrt[3]{3} \left(\int\limits_{-2}^{22} \left(- \frac{\sqrt[3]{3} x^{2}}{\left(x + 2\right)^{\frac{2}{3}}}\right)\, dx + \int\limits_{-2}^{22} \frac{2 x^{2}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx + \int\limits_{-2}^{22} \frac{2 x^{3}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx\right)}{9}$$
=
=
/ 22 22 22 \
| / / / |
| | | | |
| | 2 | 3 | 3 ___ 2 |
3 ___ | | 2*x | 2*x | -\/ 3 *x |
\/ 3 *| | ----------------- dx + | ----------------- dx + | ---------- dx|
| | 2/3 | 2/3 | 2/3 |
| | / 2 \ | / 2 \ | (2 + x) |
| | \4 + x + 2*x/ | \4 + x + 2*x/ | |
| | | / |
|/ / -2 |
\-2 -2 /
-------------------------------------------------------------------------------
9
$$\frac{\sqrt[3]{3} \left(\int\limits_{-2}^{22} \left(- \frac{\sqrt[3]{3} x^{2}}{\left(x + 2\right)^{\frac{2}{3}}}\right)\, dx + \int\limits_{-2}^{22} \frac{2 x^{2}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx + \int\limits_{-2}^{22} \frac{2 x^{3}}{\left(x^{2} + 2 x + 4\right)^{\frac{2}{3}}}\, dx\right)}{9}$$
3^(1/3)*(Integral(2*x^2/(4 + x^2 + 2*x)^(2/3), (x, -2, 22)) + Integral(2*x^3/(4 + x^2 + 2*x)^(2/3), (x, -2, 22)) + Integral(-3^(1/3)*x^2/(2 + x)^(2/3), (x, -2, 22)))/9
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.