Sr Examen
Integral de (x^3-1)/(x^4+x^2+5) dx
Solución
Ha introducido
[src]
oo / | | 3 | x - 1 | ----------- dx | 4 2 | x + x + 5 | / 1
$$\int\limits_{1}^{\infty} \frac{x^{3} - 1}{\left(x^{4} + x^{2}\right) + 5}\, dx$$
Integral((x^3 - 1)/(x^4 + x^2 + 5), (x, 1, oo))
Respuesta (Indefinida)
[src]
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$$\int \frac{x^{3} - 1}{\left(x^{4} + x^{2}\right) + 5}\, dx = C + \frac{\log{\left(2 x^{4} + 2 x^{2} + 10 \right)}}{4} - \sqrt{\frac{1}{1520} + \frac{\sqrt{5}}{760}} \log{\left(x^{2} + x \left(- \frac{4 \sqrt{19} \sqrt{1 + 2 \sqrt{5}}}{19} + \frac{3 \sqrt{95} \sqrt{1 + 2 \sqrt{5}} \sqrt{4 \sqrt{5} + 21}}{190} + \frac{17 \sqrt{95} \sqrt{1 + 2 \sqrt{5}}}{190}\right) - \frac{69 \sqrt{4 \sqrt{5} + 21}}{95} - \frac{166}{95} + \frac{47 \sqrt{5} \sqrt{4 \sqrt{5} + 21}}{190} + \frac{419 \sqrt{5}}{190} \right)} + \sqrt{\frac{1}{1520} + \frac{\sqrt{5}}{760}} \log{\left(x^{2} + x \left(- \frac{17 \sqrt{95} \sqrt{1 + 2 \sqrt{5}}}{190} - \frac{3 \sqrt{95} \sqrt{1 + 2 \sqrt{5}} \sqrt{4 \sqrt{5} + 21}}{190} + \frac{4 \sqrt{19} \sqrt{1 + 2 \sqrt{5}}}{19}\right) - \frac{69 \sqrt{4 \sqrt{5} + 21}}{95} - \frac{166}{95} + \frac{47 \sqrt{5} \sqrt{4 \sqrt{5} + 21}}{190} + \frac{419 \sqrt{5}}{190} \right)} - \frac{\sqrt{19} \operatorname{atan}{\left(\frac{2 \sqrt{19} \left(x^{2} + \frac{1}{2}\right)}{19} \right)}}{38} - 2 \sqrt{- \frac{\sqrt{4 \sqrt{5} + 21}}{760} + \frac{1}{1520} + \frac{3 \sqrt{5}}{760}} \operatorname{atan}{\left(\frac{4 \sqrt{95} x}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} - \frac{17 \sqrt{1 + 2 \sqrt{5}}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} - \frac{3 \sqrt{1 + 2 \sqrt{5}} \sqrt{4 \sqrt{5} + 21}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} + \frac{8 \sqrt{5} \sqrt{1 + 2 \sqrt{5}}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} \right)} - 2 \sqrt{- \frac{\sqrt{4 \sqrt{5} + 21}}{760} + \frac{1}{1520} + \frac{3 \sqrt{5}}{760}} \operatorname{atan}{\left(\frac{4 \sqrt{95} x}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} - \frac{8 \sqrt{5} \sqrt{1 + 2 \sqrt{5}}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} + \frac{3 \sqrt{1 + 2 \sqrt{5}} \sqrt{4 \sqrt{5} + 21}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} + \frac{17 \sqrt{1 + 2 \sqrt{5}}}{\sqrt{4 \sqrt{5} + 21} \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}} + 19 \sqrt{- 2 \sqrt{4 \sqrt{5} + 21} + 1 + 6 \sqrt{5}}} \right)}$$
Gráfica
Respuesta
[src]
oo / | | 3 | -1 + x | ----------- dx | 2 4 | 5 + x + x | / 1
$$\int\limits_{1}^{\infty} \frac{x^{3} - 1}{x^{4} + x^{2} + 5}\, dx$$
=
=
oo / | | 3 | -1 + x | ----------- dx | 2 4 | 5 + x + x | / 1
$$\int\limits_{1}^{\infty} \frac{x^{3} - 1}{x^{4} + x^{2} + 5}\, dx$$
Integral((-1 + x^3)/(5 + x^2 + x^4), (x, 1, oo))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.