Sr Examen
Integral de 1/(2*x^2+3*x^3+1) dx
Solución
Ha introducido
[src]
oo / | | 1 | --------------- dx | 2 3 | 2*x + 3*x + 1 | / 1
$$\int\limits_{1}^{\infty} \frac{1}{\left(3 x^{3} + 2 x^{2}\right) + 1}\, dx$$
Integral(1/(2*x^2 + 3*x^3 + 1), (x, 1, oo))
Respuesta (Indefinida)
[src]
/ ____ \ / ____ |6*\/ 11 *(-1/6 + x)| | / 2\ 7*\/ 11 *atan|-------------------| | 1 log\1 - x + 3*x / log(1 + x) \ 11 / | --------------- dx = C - ----------------- + ---------- + ---------------------------------- | 2 3 10 5 55 | 2*x + 3*x + 1 | /
$$\int \frac{1}{\left(3 x^{3} + 2 x^{2}\right) + 1}\, dx = C + \frac{\log{\left(x + 1 \right)}}{5} - \frac{\log{\left(3 x^{2} - x + 1 \right)}}{10} + \frac{7 \sqrt{11} \operatorname{atan}{\left(\frac{6 \sqrt{11} \left(x - \frac{1}{6}\right)}{11} \right)}}{55}$$
Gráfica
Respuesta
[src]
/ ____\
____ |5*\/ 11 |
7*\/ 11 *atan|--------| ____
log(2) \ 11 / 7*pi*\/ 11
- ------ - ----------------------- + -----------
5 55 110
$$- \frac{7 \sqrt{11} \operatorname{atan}{\left(\frac{5 \sqrt{11}}{11} \right)}}{55} - \frac{\log{\left(2 \right)}}{5} + \frac{7 \sqrt{11} \pi}{110}$$
=
=
/ ____\
____ |5*\/ 11 |
7*\/ 11 *atan|--------| ____
log(2) \ 11 / 7*pi*\/ 11
- ------ - ----------------------- + -----------
5 55 110
$$- \frac{7 \sqrt{11} \operatorname{atan}{\left(\frac{5 \sqrt{11}}{11} \right)}}{55} - \frac{\log{\left(2 \right)}}{5} + \frac{7 \sqrt{11} \pi}{110}$$
-log(2)/5 - 7*sqrt(11)*atan(5*sqrt(11)/11)/55 + 7*pi*sqrt(11)/110
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.