Sr Examen
Integral de (x^3+8x^2+12x+4)/(x+2)^2/(x^2+4) dx
Solución
Ha introducido
[src]
1 / | | / 3 2 \ | |x + 8*x + 12*x + 4| | |--------------------| | | 2 | | \ (x + 2) / | ---------------------- dx | 2 | x + 4 | / 0
$$\int\limits_{0}^{1} \frac{\left(\left(12 x + \left(x^{3} + 8 x^{2}\right)\right) + 4\right) \frac{1}{\left(x + 2\right)^{2}}}{x^{2} + 4}\, dx$$
Integral(((x^3 + 8*x^2 + 12*x + 4)/(x + 2)^2)/(x^2 + 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | / 3 2 \ | |x + 8*x + 12*x + 4| | |--------------------| | | 2 | / 2\ | \ (x + 2) / 3*log(2 + x) 1 7*log\4 + x / /x\ | ---------------------- dx = C - ------------ - --------- + ------------- + atan|-| | 2 4 2*(2 + x) 8 \2/ | x + 4 | /
$$\int \frac{\left(\left(12 x + \left(x^{3} + 8 x^{2}\right)\right) + 4\right) \frac{1}{\left(x + 2\right)^{2}}}{x^{2} + 4}\, dx = C - \frac{3 \log{\left(x + 2 \right)}}{4} + \frac{7 \log{\left(x^{2} + 4 \right)}}{8} + \operatorname{atan}{\left(\frac{x}{2} \right)} - \frac{1}{2 \left(x + 2\right)}$$
Gráfica
Respuesta
[src]
1 7*log(4) 3*log(3) 3*log(2) 7*log(5) -- - -------- - -------- + -------- + -------- + atan(1/2) 12 8 4 4 8
$$- \frac{7 \log{\left(4 \right)}}{8} - \frac{3 \log{\left(3 \right)}}{4} + \frac{1}{12} + \operatorname{atan}{\left(\frac{1}{2} \right)} + \frac{3 \log{\left(2 \right)}}{4} + \frac{7 \log{\left(5 \right)}}{8}$$
=
=
1 7*log(4) 3*log(3) 3*log(2) 7*log(5) -- - -------- - -------- + -------- + -------- + atan(1/2) 12 8 4 4 8
$$- \frac{7 \log{\left(4 \right)}}{8} - \frac{3 \log{\left(3 \right)}}{4} + \frac{1}{12} + \operatorname{atan}{\left(\frac{1}{2} \right)} + \frac{3 \log{\left(2 \right)}}{4} + \frac{7 \log{\left(5 \right)}}{8}$$
1/12 - 7*log(4)/8 - 3*log(3)/4 + 3*log(2)/4 + 7*log(5)/8 + atan(1/2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.