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