Sr Examen
Integral de sqrt(1-(2sqrt(8-4x))/3) dx
Solución
Ha introducido
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2 / | | ___________________ | / _________ | / 2*\/ 8 - 4*x | / 1 - ------------- dx | \/ 3 | / 0
$$\int\limits_{0}^{2} \sqrt{- \frac{2 \sqrt{8 - 4 x}}{3} + 1}\, dx$$
Integral(sqrt(1 - 2*sqrt(8 - 4*x)/3), (x, 0, 2))
Solución detallada
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Vuelva a escribir el integrando:
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La integral del producto de una función por una constante es la constante por la integral de esta función:
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No puedo encontrar los pasos en la búsqueda de esta integral.
Pero la integral
Por lo tanto, el resultado es:
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Añadimos la constante de integración:
Respuesta:
Respuesta (Indefinida)
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/ | _________________
| ___ | / _______
| ___________________ \/ 3 * | \/ 3 - 4*\/ 2 - x dx
| / _________ |
| / 2*\/ 8 - 4*x /
| / 1 - ------------- dx = C + --------------------------------
| \/ 3 3
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$$\int \sqrt{- \frac{2 \sqrt{8 - 4 x}}{3} + 1}\, dx = C + \frac{\sqrt{3} \int \sqrt{3 - 4 \sqrt{2 - x}}\, dx}{3}$$
Respuesta
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2 / | | / _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ | | / pi*I / pi*I / pi*I pi*I / pi*I / pi*I pi*I / pi*I / pi*I pi*I / pi*I pi*I | | / ---- / ---- / ---- ---- / ---- / ---- ---- / ---- / ---- ---- / ---- ---- | | ___ / ________ 2 3/2 / ________ 2 5/2 ___ 3/2 / ________ 2 5/2 / ___ ___ 3/2\ 2 2 / ________ 2 ___ 2 / ___ ___ 3/2\ / ________ 2 7/2 / ___ ___ 3/2\ 3 2 / ________ 2 2 ___ 5/2 / ___ ___ 3/2\ / ________ 2 2 / ___ ___ 3/2\ 3/2 2 / ________ 2 3 / ___ ___ 3/2\ 5/2 2 ________ | | 9*\/ 3 *(-4 + 2*x) 15*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 112*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 30*I*\/ 3 *(-2 + x) 6*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 6*(-2 + x) *e 9*I*\/ -3 + 4*\/ -2 + x *e *(-4 + 2*x) 9*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*(-2 + x) *e 96*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 12*I*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*I*(-2 + x) *e 32*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*I*(-2 + x) *e 4*\/ -2 + x | |--------------------------------------------- + --------------------------------------------- + ---------------------------------------------- - --------------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------- + ----------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------- - ---------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ for ------------ > 1 | | ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 2 _________________________ ___ 2 ___ 5/2 2 2 _________________________ ___ 2 ___ 5/2 2 2 _________________________ 2 _________________________ 3 | |- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I / ___ 2 ___ 5/2\ / pi*I | | \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- | | / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ | | \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | < dx | | ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ | | / pi*I / pi*I / pi*I / pi*I pi*I / pi*I pi*I / pi*I pi*I pi*I / pi*I / pi*I | | / ---- / ---- / ---- / ---- ---- / ---- ---- / ---- ---- ---- / ---- / ---- | | / ________ 2 2 / ________ 2 ___ 3 / ________ 2 / ___ ___ 3/2\ ___ 3/2 2 / ________ 2 / ___ ___ 3/2\ ___ 2 / ___ ___ 3/2\ 3/2 2 3/2 / ________ 2 5/2 2 5/2 / ________ 2 3 2 ___ 5/2 / ___ ___ 3/2\ 2 2 5/2 / ________ 2 / ___ ___ 3/2\ 7/2 / ________ 2 / ___ ___ 3/2\ | | \/ 3 - 4*\/ -2 + x *e *(36 - 18*x) 96*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 9*\/ 3 *(-4 + 2*x) 32*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 30*I*\/ 3 *(-2 + x) 9*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*(-2 + x) *e 15*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 32*(-2 + x) *e 112*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 32*I*(-2 + x) *e 12*I*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 6*I*(-2 + x) *e 6*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / | | --------------------------------------------- - --------------------------------------------- + --------------------------------------------- - ------------------------------------------------------------------------------------------ - --------------------------------------------- - ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------------------- + ---------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------- - ----------------------------------------------------------------------------- - ---------------------------------------------------------------------- - ----------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------- otherwise | | ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 2 ___ 2 ___ 5/2 2 2 ________________________ ___ 2 ___ 5/2 ________________________ ___ 2 ___ 5/2 ________________________ 2 ________________________ 2 2 | | - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / pi*I / ___ 2 ___ 5/2\ / pi*I / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ | | \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- / ---- / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | | / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ | \ \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | / 0
$$\int\limits_{0}^{2} \begin{cases} \frac{32 \left(x - 2\right)^{\frac{7}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 \left(x - 2\right)^{\frac{5}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{112 \left(x - 2\right)^{\frac{5}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{12 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 i \left(x - 2\right)^{\frac{5}{2}} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{15 \left(x - 2\right)^{\frac{3}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{30 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 i \left(x - 2\right)^{\frac{3}{2}} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{32 i \left(x - 2\right)^{3} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 \left(x - 2\right)^{3} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 i \left(x - 2\right)^{2} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{96 i \left(x - 2\right)^{2} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(x - 2\right)^{2} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 \left(x - 2\right)^{2} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 i \left(2 x - 4\right) \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(2 x - 4\right)}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} & \text{for}\: \frac{4 \sqrt{x - 2}}{3} > 1 \\\frac{\left(36 - 18 x\right) \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{32 i \left(x - 2\right)^{\frac{7}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 i \left(x - 2\right)^{\frac{5}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{112 i \left(x - 2\right)^{\frac{5}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{12 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 \left(x - 2\right)^{\frac{5}{2}} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{15 i \left(x - 2\right)^{\frac{3}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{30 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \left(x - 2\right)^{\frac{3}{2}} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} - \frac{32 \left(x - 2\right)^{3} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{32 i \left(x - 2\right)^{3} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} - \frac{9 \left(x - 2\right)^{2} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{96 \left(x - 2\right)^{2} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(x - 2\right)^{2} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{6 i \left(x - 2\right)^{2} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 \sqrt{3} \left(2 x - 4\right)}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} & \text{otherwise} \end{cases}\, dx$$
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2 / | | / _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ _________________________ | | / pi*I / pi*I / pi*I pi*I / pi*I / pi*I pi*I / pi*I / pi*I pi*I / pi*I pi*I | | / ---- / ---- / ---- ---- / ---- / ---- ---- / ---- / ---- ---- / ---- ---- | | ___ / ________ 2 3/2 / ________ 2 5/2 ___ 3/2 / ________ 2 5/2 / ___ ___ 3/2\ 2 2 / ________ 2 ___ 2 / ___ ___ 3/2\ / ________ 2 7/2 / ___ ___ 3/2\ 3 2 / ________ 2 2 ___ 5/2 / ___ ___ 3/2\ / ________ 2 2 / ___ ___ 3/2\ 3/2 2 / ________ 2 3 / ___ ___ 3/2\ 5/2 2 ________ | | 9*\/ 3 *(-4 + 2*x) 15*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 112*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 30*I*\/ 3 *(-2 + x) 6*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 6*(-2 + x) *e 9*I*\/ -3 + 4*\/ -2 + x *e *(-4 + 2*x) 9*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*(-2 + x) *e 96*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) 12*I*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*I*(-2 + x) *e 32*I*\/ -3 + 4*\/ -2 + x *e *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*I*(-2 + x) *e 4*\/ -2 + x | |--------------------------------------------- + --------------------------------------------- + ---------------------------------------------- - --------------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------- + ----------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------- - ---------------------------------------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------ for ------------ > 1 | | ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 2 _________________________ ___ 2 ___ 5/2 2 2 _________________________ ___ 2 ___ 5/2 2 2 _________________________ 2 _________________________ 3 | |- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I / ___ 2 ___ 5/2\ / pi*I | | \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- | | / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ | | \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ -3 + 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | < dx | | ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ | | / pi*I / pi*I / pi*I / pi*I pi*I / pi*I pi*I / pi*I pi*I pi*I / pi*I / pi*I | | / ---- / ---- / ---- / ---- ---- / ---- ---- / ---- ---- ---- / ---- / ---- | | / ________ 2 2 / ________ 2 ___ 3 / ________ 2 / ___ ___ 3/2\ ___ 3/2 2 / ________ 2 / ___ ___ 3/2\ ___ 2 / ___ ___ 3/2\ 3/2 2 3/2 / ________ 2 5/2 2 5/2 / ________ 2 3 2 ___ 5/2 / ___ ___ 3/2\ 2 2 5/2 / ________ 2 / ___ ___ 3/2\ 7/2 / ________ 2 / ___ ___ 3/2\ | | \/ 3 - 4*\/ -2 + x *e *(36 - 18*x) 96*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 9*\/ 3 *(-4 + 2*x) 32*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 30*I*\/ 3 *(-2 + x) 9*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 9*(-2 + x) *e 15*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 32*(-2 + x) *e 112*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e 32*I*(-2 + x) *e 12*I*\/ 3 *(-2 + x) *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 6*I*(-2 + x) *e 6*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / 32*I*(-2 + x) *\/ 3 - 4*\/ -2 + x *e *\30*\/ 3 *(-4 + 2*x) - 100*I*\/ 3 *(-2 + x) / | | --------------------------------------------- - --------------------------------------------- + --------------------------------------------- - ------------------------------------------------------------------------------------------ - --------------------------------------------- - ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------- + ----------------------------------------------------------------------------- + ---------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------- - ----------------------------------------------------------------------------- - ---------------------------------------------------------------------- - ----------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------- otherwise | | ___ 2 ___ 5/2 ___ 2 ___ 5/2 ___ 2 ___ 5/2 2 ___ 2 ___ 5/2 2 2 ________________________ ___ 2 ___ 5/2 ________________________ ___ 2 ___ 5/2 ________________________ 2 ________________________ 2 2 | | - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / pi*I - 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / pi*I / ___ 2 ___ 5/2\ / pi*I / ___ 2 ___ 5/2\ / ___ 2 ___ 5/2\ | | \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- / ---- / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / / ---- \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | | / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ / ________ 2 / ___ 2 ___ 5/2\ | \ \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / \/ 3 - 4*\/ -2 + x *e *\- 30*\/ 3 *(-2 + x) + 40*I*\/ 3 *(-2 + x) / | / 0
$$\int\limits_{0}^{2} \begin{cases} \frac{32 \left(x - 2\right)^{\frac{7}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 \left(x - 2\right)^{\frac{5}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{112 \left(x - 2\right)^{\frac{5}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{12 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 i \left(x - 2\right)^{\frac{5}{2}} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{15 \left(x - 2\right)^{\frac{3}{2}} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{30 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 i \left(x - 2\right)^{\frac{3}{2}} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{32 i \left(x - 2\right)^{3} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 \left(x - 2\right)^{3} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 i \left(x - 2\right)^{2} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{96 i \left(x - 2\right)^{2} \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(x - 2\right)^{2} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 \left(x - 2\right)^{2} e^{\frac{i \pi}{2}}}{\sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 i \left(2 x - 4\right) \sqrt{4 \sqrt{x - 2} e^{\frac{i \pi}{2}} - 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(2 x - 4\right)}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} & \text{for}\: \frac{4 \sqrt{x - 2}}{3} > 1 \\\frac{\left(36 - 18 x\right) \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{32 i \left(x - 2\right)^{\frac{7}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{6 i \left(x - 2\right)^{\frac{5}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{112 i \left(x - 2\right)^{\frac{5}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{12 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} + \frac{32 \left(x - 2\right)^{\frac{5}{2}} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{15 i \left(x - 2\right)^{\frac{3}{2}} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} - \frac{30 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \left(x - 2\right)^{\frac{3}{2}} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} - \frac{32 \left(x - 2\right)^{3} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{32 i \left(x - 2\right)^{3} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} - \frac{9 \left(x - 2\right)^{2} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{96 \left(x - 2\right)^{2} \sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3}}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} + \frac{9 \sqrt{3} \left(x - 2\right)^{2} \left(- 100 \sqrt{3} i \left(x - 2\right)^{\frac{3}{2}} + 30 \sqrt{3} \left(2 x - 4\right)\right)}{\left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)^{2}} - \frac{6 i \left(x - 2\right)^{2} e^{\frac{i \pi}{2}}}{\sqrt{- 4 \sqrt{x - 2} e^{\frac{i \pi}{2}} + 3} \left(40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}\right)} + \frac{9 \sqrt{3} \left(2 x - 4\right)}{40 \sqrt{3} i \left(x - 2\right)^{\frac{5}{2}} - 30 \sqrt{3} \left(x - 2\right)^{2}} & \text{otherwise} \end{cases}\, dx$$
Integral(Piecewise((9*sqrt(3)*(-4 + 2*x)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 15*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^(3/2)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 112*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^(5/2)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 30*i*sqrt(3)*(-2 + x)^(3/2)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 6*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^(5/2)*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 6*(-2 + x)^2*exp_polar(pi*i/2)/(sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 9*i*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-4 + 2*x)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 9*sqrt(3)*(-2 + x)^2*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 32*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^(7/2)*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 32*(-2 + x)^3*exp_polar(pi*i/2)/(sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 96*i*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^2/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 12*i*sqrt(3)*(-2 + x)^(5/2)*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 9*i*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^2*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 9*i*(-2 + x)^(3/2)*exp_polar(pi*i/2)/(sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 32*i*sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-2 + x)^3*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 32*i*(-2 + x)^(5/2)*exp_polar(pi*i/2)/(sqrt(-3 + 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))), 4*sqrt(-2 + x)/3 > 1), (sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(36 - 18*x)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 96*(-2 + x)^2*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 9*sqrt(3)*(-4 + 2*x)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 32*(-2 + x)^3*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 - 30*i*sqrt(3)*(-2 + x)^(3/2)/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 9*(-2 + x)^2*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 9*sqrt(3)*(-2 + x)^2*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 9*(-2 + x)^(3/2)*exp_polar(pi*i/2)/(sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 15*i*(-2 + x)^(3/2)*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) + 32*(-2 + x)^(5/2)*exp_polar(pi*i/2)/(sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 112*i*(-2 + x)^(5/2)*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2)) - 32*i*(-2 + x)^3*exp_polar(pi*i/2)/(sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) - 12*i*sqrt(3)*(-2 + x)^(5/2)*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 - 6*i*(-2 + x)^2*exp_polar(pi*i/2)/(sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))) + 6*i*(-2 + x)^(5/2)*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2 + 32*i*(-2 + x)^(7/2)*sqrt(3 - 4*sqrt(-2 + x)*exp_polar(pi*i/2))*(30*sqrt(3)*(-4 + 2*x) - 100*i*sqrt(3)*(-2 + x)^(3/2))/(-30*sqrt(3)*(-2 + x)^2 + 40*i*sqrt(3)*(-2 + x)^(5/2))^2, True)), (x, 0, 2))
Respuesta numérica
[src]
(0.300189162083732 + 0.956937530079808j)
(0.300189162083732 + 0.956937530079808j)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.