Sr Examen
Integral de ((x^3)-1)/(3*(x^4)+x^2+5) dx
Solución
Ha introducido
[src]
oo / | | 3 | x - 1 | ------------- dx | 4 2 | 3*x + x + 5 | / 1
$$\int\limits_{1}^{\infty} \frac{x^{3} - 1}{\left(3 x^{4} + x^{2}\right) + 5}\, dx$$
Integral((x^3 - 1)/(3*x^4 + x^2 + 5), (x, 1, oo))
Respuesta (Indefinida)
[src]
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$$\int \frac{x^{3} - 1}{\left(3 x^{4} + x^{2}\right) + 5}\, dx = C + \frac{\log{\left(6 x^{4} + 2 x^{2} + 10 \right)}}{12} - \sqrt{\frac{1}{4720} + \frac{\sqrt{15}}{2360}} \log{\left(x^{2} + x \left(- \frac{4 \sqrt{177} \sqrt{1 + 2 \sqrt{15}}}{177} + \frac{\sqrt{295} \sqrt{1 + 2 \sqrt{15}} \sqrt{4 \sqrt{15} + 61}}{590} + \frac{19 \sqrt{295} \sqrt{1 + 2 \sqrt{15}}}{590}\right) - \frac{56 \sqrt{4 \sqrt{15} + 61}}{295} - \frac{667}{885} + \frac{167 \sqrt{15} \sqrt{4 \sqrt{15} + 61}}{5310} + \frac{3619 \sqrt{15}}{5310} \right)} + \sqrt{\frac{1}{4720} + \frac{\sqrt{15}}{2360}} \log{\left(x^{2} + x \left(- \frac{19 \sqrt{295} \sqrt{1 + 2 \sqrt{15}}}{590} - \frac{\sqrt{295} \sqrt{1 + 2 \sqrt{15}} \sqrt{4 \sqrt{15} + 61}}{590} + \frac{4 \sqrt{177} \sqrt{1 + 2 \sqrt{15}}}{177}\right) - \frac{56 \sqrt{4 \sqrt{15} + 61}}{295} - \frac{667}{885} + \frac{167 \sqrt{15} \sqrt{4 \sqrt{15} + 61}}{5310} + \frac{3619 \sqrt{15}}{5310} \right)} - \frac{\sqrt{59} \operatorname{atan}{\left(\frac{6 \sqrt{59} \left(x^{2} + \frac{1}{6}\right)}{59} \right)}}{354} - 2 \sqrt{- \frac{\sqrt{4 \sqrt{15} + 61}}{2360} + \frac{1}{4720} + \frac{3 \sqrt{15}}{2360}} \operatorname{atan}{\left(\frac{12 \sqrt{295} x}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} - \frac{57 \sqrt{1 + 2 \sqrt{15}}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} - \frac{3 \sqrt{1 + 2 \sqrt{15}} \sqrt{4 \sqrt{15} + 61}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} + \frac{8 \sqrt{15} \sqrt{1 + 2 \sqrt{15}}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} \right)} - 2 \sqrt{- \frac{\sqrt{4 \sqrt{15} + 61}}{2360} + \frac{1}{4720} + \frac{3 \sqrt{15}}{2360}} \operatorname{atan}{\left(\frac{12 \sqrt{295} x}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} - \frac{8 \sqrt{15} \sqrt{1 + 2 \sqrt{15}}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} + \frac{3 \sqrt{1 + 2 \sqrt{15}} \sqrt{4 \sqrt{15} + 61}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} + \frac{57 \sqrt{1 + 2 \sqrt{15}}}{\sqrt{4 \sqrt{15} + 61} \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}} + 59 \sqrt{- 2 \sqrt{4 \sqrt{15} + 61} + 1 + 6 \sqrt{15}}} \right)}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.