Sr Examen
Integral de (x^3+6x^2+9x+6)/((x+1)^2(x^2+2x+2)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | x + 6*x + 9*x + 6 | ----------------------- dx | 2 / 2 \ | (x + 1) *\x + 2*x + 2/ | / 0
$$\int\limits_{0}^{1} \frac{\left(9 x + \left(x^{3} + 6 x^{2}\right)\right) + 6}{\left(x + 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 2\right)}\, dx$$
Integral((x^3 + 6*x^2 + 9*x + 6)/(((x + 1)^2*(x^2 + 2*x + 2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 3 2 / 2 \ | x + 6*x + 9*x + 6 log\2 + x + 2*x/ 2 | ----------------------- dx = C + ----------------- - ----- + atan(1 + x) | 2 / 2 \ 2 1 + x | (x + 1) *\x + 2*x + 2/ | /
$$\int \frac{\left(9 x + \left(x^{3} + 6 x^{2}\right)\right) + 6}{\left(x + 1\right)^{2} \left(\left(x^{2} + 2 x\right) + 2\right)}\, dx = C + \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} + \operatorname{atan}{\left(x + 1 \right)} - \frac{2}{x + 1}$$
Gráfica
Respuesta
[src]
log(5) log(2) pi
1 + ------ - ------ - -- + atan(2)
2 2 4
$$- \frac{\pi}{4} - \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(5 \right)}}{2} + 1 + \operatorname{atan}{\left(2 \right)}$$
=
=
log(5) log(2) pi
1 + ------ - ------ - -- + atan(2)
2 2 4
$$- \frac{\pi}{4} - \frac{\log{\left(2 \right)}}{2} + \frac{\log{\left(5 \right)}}{2} + 1 + \operatorname{atan}{\left(2 \right)}$$
1 + log(5)/2 - log(2)/2 - pi/4 + atan(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.