Sr Examen
Integral de xdx/sqr(1-3x*x-2x*x*x*x) dx
Solución
Ha introducido
[src]
1 / | | x | ------------------------ dx | 2 | (1 - 3*x*x - 2*x*x*x*x) | / 0
$$\int\limits_{0}^{1} \frac{x}{\left(- x x x 2 x + \left(- x 3 x + 1\right)\right)^{2}}\, dx$$
Integral(x/(1 - 3*x*x - ((2*x)*x)*x*x)^2, (x, 0, 1))
Gráfica
Respuesta
[src]
/ / ____\ / ____\\ / / ____\ / ____\\ / / ____\\
| ____ |3 2 \/ 17 | ____ |3 2 \/ 17 || | ____ |3 2 \/ 17 | ____ |3 2 \/ 17 || ____ | | 3 \/ 17 ||
| 2 2*\/ 17 *log|- + x - ------| 2*\/ 17 *log|- + x + ------|| | 2 2*\/ 17 *log|- + x - ------| 2*\/ 17 *log|- + x + ------|| 2*\/ 17 *|pi*I + log|- - + ------||
| 3 + 4*x \4 4 / \4 4 /| | 3 + 4*x \4 4 / \4 4 /| \ \ 4 4 //
oo - lim |- -------------------- - ----------------------------- + -----------------------------| - lim |- -------------------- - ----------------------------- + -----------------------------| + -----------------------------------
______________ | 4 2 289 289 | _____________ | 4 2 289 289 | 289
/ ____ \ -34 + 68*x + 102*x / / ____ \ -34 + 68*x + 102*x /
/ 3 \/ 17 \/ -3 + \/ 17
x-> / - - + ------ + x->----------------+
\/ 4 4 2
$$\infty + \frac{2 \sqrt{17} \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{17}}{4} \right)} + i \pi\right)}{289} - \lim_{x \to \frac{\sqrt{-3 + \sqrt{17}}}{2}^+}\left(- \frac{4 x^{2} + 3}{68 x^{4} + 102 x^{2} - 34} + \frac{2 \sqrt{17} \log{\left(x^{2} + \frac{3}{4} + \frac{\sqrt{17}}{4} \right)}}{289} - \frac{2 \sqrt{17} \log{\left(x^{2} - \frac{\sqrt{17}}{4} + \frac{3}{4} \right)}}{289}\right) - \lim_{x \to \sqrt{- \frac{3}{4} + \frac{\sqrt{17}}{4}}^+}\left(- \frac{4 x^{2} + 3}{68 x^{4} + 102 x^{2} - 34} + \frac{2 \sqrt{17} \log{\left(x^{2} + \frac{3}{4} + \frac{\sqrt{17}}{4} \right)}}{289} - \frac{2 \sqrt{17} \log{\left(x^{2} - \frac{\sqrt{17}}{4} + \frac{3}{4} \right)}}{289}\right)$$
=
=
/ / ____\ / ____\\ / / ____\ / ____\\ / / ____\\
| ____ |3 2 \/ 17 | ____ |3 2 \/ 17 || | ____ |3 2 \/ 17 | ____ |3 2 \/ 17 || ____ | | 3 \/ 17 ||
| 2 2*\/ 17 *log|- + x - ------| 2*\/ 17 *log|- + x + ------|| | 2 2*\/ 17 *log|- + x - ------| 2*\/ 17 *log|- + x + ------|| 2*\/ 17 *|pi*I + log|- - + ------||
| 3 + 4*x \4 4 / \4 4 /| | 3 + 4*x \4 4 / \4 4 /| \ \ 4 4 //
oo - lim |- -------------------- - ----------------------------- + -----------------------------| - lim |- -------------------- - ----------------------------- + -----------------------------| + -----------------------------------
______________ | 4 2 289 289 | _____________ | 4 2 289 289 | 289
/ ____ \ -34 + 68*x + 102*x / / ____ \ -34 + 68*x + 102*x /
/ 3 \/ 17 \/ -3 + \/ 17
x-> / - - + ------ + x->----------------+
\/ 4 4 2
$$\infty + \frac{2 \sqrt{17} \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{17}}{4} \right)} + i \pi\right)}{289} - \lim_{x \to \frac{\sqrt{-3 + \sqrt{17}}}{2}^+}\left(- \frac{4 x^{2} + 3}{68 x^{4} + 102 x^{2} - 34} + \frac{2 \sqrt{17} \log{\left(x^{2} + \frac{3}{4} + \frac{\sqrt{17}}{4} \right)}}{289} - \frac{2 \sqrt{17} \log{\left(x^{2} - \frac{\sqrt{17}}{4} + \frac{3}{4} \right)}}{289}\right) - \lim_{x \to \sqrt{- \frac{3}{4} + \frac{\sqrt{17}}{4}}^+}\left(- \frac{4 x^{2} + 3}{68 x^{4} + 102 x^{2} - 34} + \frac{2 \sqrt{17} \log{\left(x^{2} + \frac{3}{4} + \frac{\sqrt{17}}{4} \right)}}{289} - \frac{2 \sqrt{17} \log{\left(x^{2} - \frac{\sqrt{17}}{4} + \frac{3}{4} \right)}}{289}\right)$$
oo - Limit(-(3 + 4*x^2)/(-34 + 68*x^4 + 102*x^2) - 2*sqrt(17)*log(3/4 + x^2 - sqrt(17)/4)/289 + 2*sqrt(17)*log(3/4 + x^2 + sqrt(17)/4)/289, x, sqrt(-3/4 + sqrt(17)/4)) - Limit(-(3 + 4*x^2)/(-34 + 68*x^4 + 102*x^2) - 2*sqrt(17)*log(3/4 + x^2 - sqrt(17)/4)/289 + 2*sqrt(17)*log(3/4 + x^2 + sqrt(17)/4)/289, x, sqrt(-3 + sqrt(17))/2) + 2*sqrt(17)*(pi*i + log(-3/4 + sqrt(17)/4))/289
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.