Sr Examen
Integral de (2x^3-7x^2+12x-27)/((x-2)(x^2-x+3)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | 2*x - 7*x + 12*x - 27 | ----------------------- dx | / 2 \ | (x - 2)*\x - x + 3/ | / 0
$$\int\limits_{0}^{1} \frac{\left(12 x + \left(2 x^{3} - 7 x^{2}\right)\right) - 27}{\left(x - 2\right) \left(\left(x^{2} - x\right) + 3\right)}\, dx$$
Integral((2*x^3 - 7*x^2 + 12*x - 27)/(((x - 2)*(x^2 - x + 3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / ____ \ | ____ |2*\/ 11 *(-1/2 + x)| | 3 2 8*\/ 11 *atan|-------------------| | 2*x - 7*x + 12*x - 27 \ 11 / / 2 \ | ----------------------- dx = C - 3*log(-2 + x) + 2*x + ---------------------------------- + log\3 + x - x/ | / 2 \ 11 | (x - 2)*\x - x + 3/ | /
$$\int \frac{\left(12 x + \left(2 x^{3} - 7 x^{2}\right)\right) - 27}{\left(x - 2\right) \left(\left(x^{2} - x\right) + 3\right)}\, dx = C + 2 x - 3 \log{\left(x - 2 \right)} + \log{\left(x^{2} - x + 3 \right)} + \frac{8 \sqrt{11} \operatorname{atan}{\left(\frac{2 \sqrt{11} \left(x - \frac{1}{2}\right)}{11} \right)}}{11}$$
Gráfica
Respuesta
[src]
/ ____\
____ |\/ 11 |
16*\/ 11 *atan|------|
\ 11 /
2 + 3*log(2) + ----------------------
11
$$\frac{16 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} + 2 + 3 \log{\left(2 \right)}$$
=
=
/ ____\
____ |\/ 11 |
16*\/ 11 *atan|------|
\ 11 /
2 + 3*log(2) + ----------------------
11
$$\frac{16 \sqrt{11} \operatorname{atan}{\left(\frac{\sqrt{11}}{11} \right)}}{11} + 2 + 3 \log{\left(2 \right)}$$
2 + 3*log(2) + 16*sqrt(11)*atan(sqrt(11)/11)/11
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.