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