Sr Examen
Integral de (2x-3x^2)/(7-5x^4) dx
Solución
Ha introducido
[src]
1 / | | 2 | 2*x - 3*x | ---------- dx | 4 | 7 - 5*x | / 0
$$\int\limits_{0}^{1} \frac{- 3 x^{2} + 2 x}{7 - 5 x^{4}}\, dx$$
Integral((2*x - 3*x^2)/(7 - 5*x^4), (x, 0, 1))
Respuesta (Indefinida)
[src]
// / ____ 2\ \
|| ____ |\/ 35 *x | |
/ ||-\/ 35 *acoth|---------| | / 4 _____\ / 4 ______\ / 4 _____\
| || \ 7 / 4 | 4 ______ | \/ 875 | 4 ______ |x*\/ 1715 | 4 ______ | \/ 875 |
| 2 ||------------------------- for x > 7/5| 3*\/ 1715 *log|x + -------| 3*\/ 1715 *atan|----------| 3*\/ 1715 *log|x - -------|
| 2*x - 3*x || 70 | \ 5 / \ 7 / \ 5 /
| ---------- dx = C - 2*|< | - --------------------------- + --------------------------- + ---------------------------
| 4 || / ____ 2\ | 140 70 140
| 7 - 5*x || ____ |\/ 35 *x | |
| ||-\/ 35 *atanh|---------| |
/ || \ 7 / 4 |
||------------------------- for x < 7/5|
\\ 70 /
$$\int \frac{- 3 x^{2} + 2 x}{7 - 5 x^{4}}\, dx = C - 2 \left(\begin{cases} - \frac{\sqrt{35} \operatorname{acoth}{\left(\frac{\sqrt{35} x^{2}}{7} \right)}}{70} & \text{for}\: x^{4} > \frac{7}{5} \\- \frac{\sqrt{35} \operatorname{atanh}{\left(\frac{\sqrt{35} x^{2}}{7} \right)}}{70} & \text{for}\: x^{4} < \frac{7}{5} \end{cases}\right) + \frac{3 \sqrt[4]{1715} \log{\left(x - \frac{\sqrt[4]{875}}{5} \right)}}{140} - \frac{3 \sqrt[4]{1715} \log{\left(x + \frac{\sqrt[4]{875}}{5} \right)}}{140} + \frac{3 \sqrt[4]{1715} \operatorname{atan}{\left(\frac{\sqrt[4]{1715} x}{7} \right)}}{70}$$
Respuesta
[src]
/ / 3 2\\ / / 3 2\\
| 4 2 | 3722 235200*t 5040*t 44800*t || | 4 2 | 1061 235200*t 5040*t 44800*t ||
- RootSum|1568000*t - 22400*t + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------|| + RootSum|1568000*t - 22400*t + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------||
\ \ 2661 887 887 2661 // \ \ 2661 887 887 2661 //
$$- \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{3722}{2661} \right)} \right)\right)} + \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{1061}{2661} \right)} \right)\right)}$$
=
=
/ / 3 2\\ / / 3 2\\
| 4 2 | 3722 235200*t 5040*t 44800*t || | 4 2 | 1061 235200*t 5040*t 44800*t ||
- RootSum|1568000*t - 22400*t + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------|| + RootSum|1568000*t - 22400*t + 10080*t - 487, t -> t*log|- ---- - --------- + ------ + --------||
\ \ 2661 887 887 2661 // \ \ 2661 887 887 2661 //
$$- \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{3722}{2661} \right)} \right)\right)} + \operatorname{RootSum} {\left(1568000 t^{4} - 22400 t^{2} + 10080 t - 487, \left( t \mapsto t \log{\left(- \frac{235200 t^{3}}{887} + \frac{44800 t^{2}}{2661} + \frac{5040 t}{887} - \frac{1061}{2661} \right)} \right)\right)}$$
-RootSum(1568000*_t^4 - 22400*_t^2 + 10080*_t - 487, Lambda(_t, _t*log(-3722/2661 - 235200*_t^3/887 + 5040*_t/887 + 44800*_t^2/2661))) + RootSum(1568000*_t^4 - 22400*_t^2 + 10080*_t - 487, Lambda(_t, _t*log(-1061/2661 - 235200*_t^3/887 + 5040*_t/887 + 44800*_t^2/2661)))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.