Sr Examen
Integral de (3x^2+3x+22)/(((x^2+4x+8))(x-3)) dx
Solución
Ha introducido
[src]
1 / | | 2 | 3*x + 3*x + 22 | ---------------------- dx | / 2 \ | \x + 4*x + 8/*(x - 3) | / 0
$$\int\limits_{0}^{1} \frac{\left(3 x^{2} + 3 x\right) + 22}{\left(x - 3\right) \left(\left(x^{2} + 4 x\right) + 8\right)}\, dx$$
Integral((3*x^2 + 3*x + 22)/(((x^2 + 4*x + 8)*(x - 3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 2 / 2 \ | 3*x + 3*x + 22 log\8 + x + 4*x/ / x\ | ---------------------- dx = C + ----------------- - 2*atan|1 + -| + 2*log(-3 + x) | / 2 \ 2 \ 2/ | \x + 4*x + 8/*(x - 3) | /
$$\int \frac{\left(3 x^{2} + 3 x\right) + 22}{\left(x - 3\right) \left(\left(x^{2} + 4 x\right) + 8\right)}\, dx = C + 2 \log{\left(x - 3 \right)} + \frac{\log{\left(x^{2} + 4 x + 8 \right)}}{2} - 2 \operatorname{atan}{\left(\frac{x}{2} + 1 \right)}$$
Gráfica
Respuesta
[src]
pi log(13) log(8) -- + ------- - 2*atan(3/2) - 2*log(3) + 2*log(2) - ------ 2 2 2
$$- 2 \log{\left(3 \right)} - 2 \operatorname{atan}{\left(\frac{3}{2} \right)} - \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(13 \right)}}{2} + 2 \log{\left(2 \right)} + \frac{\pi}{2}$$
=
=
pi log(13) log(8) -- + ------- - 2*atan(3/2) - 2*log(3) + 2*log(2) - ------ 2 2 2
$$- 2 \log{\left(3 \right)} - 2 \operatorname{atan}{\left(\frac{3}{2} \right)} - \frac{\log{\left(8 \right)}}{2} + \frac{\log{\left(13 \right)}}{2} + 2 \log{\left(2 \right)} + \frac{\pi}{2}$$
pi/2 + log(13)/2 - 2*atan(3/2) - 2*log(3) + 2*log(2) - log(8)/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.