Sr Examen
Integral de (2x^3+10x^2+15x+4)/((x+3)^2*(x^2+2x+2)) dx
Solución
Ha introducido
[src]
1 / | | 3 2 | 2*x + 10*x + 15*x + 4 | ----------------------- dx | 2 / 2 \ | (x + 3) *\x + 2*x + 2/ | / 0
$$\int\limits_{0}^{1} \frac{\left(15 x + \left(2 x^{3} + 10 x^{2}\right)\right) + 4}{\left(x + 3\right)^{2} \left(\left(x^{2} + 2 x\right) + 2\right)}\, dx$$
Integral((2*x^3 + 10*x^2 + 15*x + 4)/(((x + 3)^2*(x^2 + 2*x + 2))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 3 2 / 2 \ | 2*x + 10*x + 15*x + 4 1 log\2 + x + 2*x/ | ----------------------- dx = C + ----- + ----------------- - atan(1 + x) + log(3 + x) | 2 / 2 \ 3 + x 2 | (x + 3) *\x + 2*x + 2/ | /
$$\int \frac{\left(15 x + \left(2 x^{3} + 10 x^{2}\right)\right) + 4}{\left(x + 3\right)^{2} \left(\left(x^{2} + 2 x\right) + 2\right)}\, dx = C + \log{\left(x + 3 \right)} + \frac{\log{\left(x^{2} + 2 x + 2 \right)}}{2} - \operatorname{atan}{\left(x + 1 \right)} + \frac{1}{x + 3}$$
Gráfica
Respuesta
[src]
1 log(5) log(2) pi - -- + ------ - atan(2) - log(3) - ------ + -- + log(4) 12 2 2 4
$$- \operatorname{atan}{\left(2 \right)} - \log{\left(3 \right)} - \frac{\log{\left(2 \right)}}{2} - \frac{1}{12} + \frac{\pi}{4} + \frac{\log{\left(5 \right)}}{2} + \log{\left(4 \right)}$$
=
=
1 log(5) log(2) pi - -- + ------ - atan(2) - log(3) - ------ + -- + log(4) 12 2 2 4
$$- \operatorname{atan}{\left(2 \right)} - \log{\left(3 \right)} - \frac{\log{\left(2 \right)}}{2} - \frac{1}{12} + \frac{\pi}{4} + \frac{\log{\left(5 \right)}}{2} + \log{\left(4 \right)}$$
-1/12 + log(5)/2 - atan(2) - log(3) - log(2)/2 + pi/4 + log(4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.