Sr Examen
Integral de 1/(5x^4+3x^2+2) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------- dx | 4 2 | 5*x + 3*x + 2 | / 2
$$\int\limits_{2}^{\infty} \frac{1}{\left(5 x^{4} + 3 x^{2}\right) + 2}\, dx$$
Integral(1/(5*x^4 + 3*x^2 + 2), (x, 2, oo))
Respuesta (Indefinida)
[src]
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2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 / \31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 31*\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 + 3*\/ 49 + 12*\/ 10 *\/ 3 - 2*\/ 49 + 12*\/ 10 + 6*\/ 10 /
$$\int \frac{1}{\left(5 x^{4} + 3 x^{2}\right) + 2}\, dx = C + \sqrt{\frac{3}{992} + \frac{\sqrt{10}}{496}} \log{\left(x^{2} + x \left(- \frac{12 \sqrt{155} \sqrt{3 + 2 \sqrt{10}}}{155} + \frac{13 \sqrt{62} \sqrt{3 + 2 \sqrt{10}}}{620} + \frac{9 \sqrt{62} \sqrt{3 + 2 \sqrt{10}} \sqrt{12 \sqrt{10} + 49}}{620}\right) - \frac{1273 \sqrt{12 \sqrt{10} + 49}}{3100} + \frac{9 \sqrt{10} \sqrt{12 \sqrt{10} + 49}}{3100} + \frac{3639}{3100} + \frac{3139 \sqrt{10}}{3100} \right)} - \sqrt{\frac{3}{992} + \frac{\sqrt{10}}{496}} \log{\left(x^{2} + x \left(- \frac{9 \sqrt{62} \sqrt{3 + 2 \sqrt{10}} \sqrt{12 \sqrt{10} + 49}}{620} - \frac{13 \sqrt{62} \sqrt{3 + 2 \sqrt{10}}}{620} + \frac{12 \sqrt{155} \sqrt{3 + 2 \sqrt{10}}}{155}\right) - \frac{1273 \sqrt{12 \sqrt{10} + 49}}{3100} + \frac{9 \sqrt{10} \sqrt{12 \sqrt{10} + 49}}{3100} + \frac{3639}{3100} + \frac{3139 \sqrt{10}}{3100} \right)} + 2 \sqrt{- \frac{\sqrt{12 \sqrt{10} + 49}}{496} + \frac{3}{992} + \frac{3 \sqrt{10}}{496}} \operatorname{atan}{\left(\frac{20 \sqrt{62} x}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} - \frac{24 \sqrt{10} \sqrt{3 + 2 \sqrt{10}}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} + \frac{13 \sqrt{3 + 2 \sqrt{10}}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} + \frac{9 \sqrt{3 + 2 \sqrt{10}} \sqrt{12 \sqrt{10} + 49}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} \right)} + 2 \sqrt{- \frac{\sqrt{12 \sqrt{10} + 49}}{496} + \frac{3}{992} + \frac{3 \sqrt{10}}{496}} \operatorname{atan}{\left(\frac{20 \sqrt{62} x}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} - \frac{9 \sqrt{3 + 2 \sqrt{10}} \sqrt{12 \sqrt{10} + 49}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} - \frac{13 \sqrt{3 + 2 \sqrt{10}}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} + \frac{24 \sqrt{10} \sqrt{3 + 2 \sqrt{10}}}{3 \sqrt{12 \sqrt{10} + 49} \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}} + 31 \sqrt{- 2 \sqrt{12 \sqrt{10} + 49} + 3 + 6 \sqrt{10}}} \right)}$$
Gráfica
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.