Sr Examen
Integral de x^2/(2*x^6+x^3+4) dx
Solución
Ha introducido
[src]
1 / | | 2 | x | ------------- dx | 6 3 | 2*x + x + 4 | / 0
$$\int\limits_{0}^{1} \frac{x^{2}}{\left(2 x^{6} + x^{3}\right) + 4}\, dx$$
Integral(x^2/(2*x^6 + x^3 + 4), (x, 0, 1))
Respuesta (Indefinida)
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/ ____ /1 3\\ / |4*\/ 31 *|- + x || | ____ | \4 /| | 2 2*\/ 31 *atan|-----------------| | x \ 31 / | ------------- dx = C + -------------------------------- | 6 3 93 | 2*x + x + 4 | /
$$\int \frac{x^{2}}{\left(2 x^{6} + x^{3}\right) + 4}\, dx = C + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{4 \sqrt{31} \left(x^{3} + \frac{1}{4}\right)}{31} \right)}}{93}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |\/ 31 | ____ |5*\/ 31 |
2*\/ 31 *atan|------| 2*\/ 31 *atan|--------|
\ 31 / \ 31 /
- --------------------- + -----------------------
93 93
$$- \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{\sqrt{31}}{31} \right)}}{93} + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{5 \sqrt{31}}{31} \right)}}{93}$$
=
=
/ ____\ / ____\
____ |\/ 31 | ____ |5*\/ 31 |
2*\/ 31 *atan|------| 2*\/ 31 *atan|--------|
\ 31 / \ 31 /
- --------------------- + -----------------------
93 93
$$- \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{\sqrt{31}}{31} \right)}}{93} + \frac{2 \sqrt{31} \operatorname{atan}{\left(\frac{5 \sqrt{31}}{31} \right)}}{93}$$
-2*sqrt(31)*atan(sqrt(31)/31)/93 + 2*sqrt(31)*atan(5*sqrt(31)/31)/93
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.