Sr Examen
Integral de (x^3+2)/(x^2-3x+5) dx
Solución
Ha introducido
[src]
1 / | | 3 | x + 2 | ------------ dx | 2 | x - 3*x + 5 | / 0
$$\int\limits_{0}^{1} \frac{x^{3} + 2}{\left(x^{2} - 3 x\right) + 5}\, dx$$
Integral((x^3 + 2)/(x^2 - 3*x + 5), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ____ \ | ____ |2*\/ 11 *(-3/2 + x)| | 3 2 14*\/ 11 *atan|-------------------| | x + 2 x / 2 \ \ 11 / | ------------ dx = C + -- + 2*log\5 + x - 3*x/ + 3*x - ----------------------------------- | 2 2 11 | x - 3*x + 5 | /
$$\int \frac{x^{3} + 2}{\left(x^{2} - 3 x\right) + 5}\, dx = C + \frac{x^{2}}{2} + 3 x + 2 \log{\left(x^{2} - 3 x + 5 \right)} - \frac{14 \sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} \left(x - \frac{3}{2}\right)}{11} \right)}}{11}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |3*\/ 11 | ____ |\/ 11 |
14*\/ 11 *atan|--------| 14*\/ 11 *atan|------|
7 \ 11 / \ 11 /
- - 2*log(5) + 2*log(3) - ------------------------ + ----------------------
2 11 11
$$- 2 \log{\left(5 \right)} - \frac{14 \sqrt{11} \operatorname{atan}{\left(\frac{3 \sqrt{11}}{11} \right)}}{11} + \frac{14 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} + 2 \log{\left(3 \right)} + \frac{7}{2}$$
=
=
/ ____\ / ____\
____ |3*\/ 11 | ____ |\/ 11 |
14*\/ 11 *atan|--------| 14*\/ 11 *atan|------|
7 \ 11 / \ 11 /
- - 2*log(5) + 2*log(3) - ------------------------ + ----------------------
2 11 11
$$- 2 \log{\left(5 \right)} - \frac{14 \sqrt{11} \operatorname{atan}{\left(\frac{3 \sqrt{11}}{11} \right)}}{11} + \frac{14 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} + 2 \log{\left(3 \right)} + \frac{7}{2}$$
7/2 - 2*log(5) + 2*log(3) - 14*sqrt(11)*atan(3*sqrt(11)/11)/11 + 14*sqrt(11)*atan(sqrt(11)/11)/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.