Sr Examen
Integral de (3*x+5)/((x+2)*(x^2+3*x+3)) dx
Solución
Ha introducido
[src]
1 / | | 3*x + 5 | ---------------------- dx | / 2 \ | (x + 2)*\x + 3*x + 3/ | / 0
$$\int\limits_{0}^{1} \frac{3 x + 5}{\left(x + 2\right) \left(\left(x^{2} + 3 x\right) + 3\right)}\, dx$$
Integral((3*x + 5)/(((x + 2)*(x^2 + 3*x + 3))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ \ / ___ |2*\/ 3 *(3/2 + x)| | / 2 \ 5*\/ 3 *atan|-----------------| | 3*x + 5 log\3 + x + 3*x/ \ 3 / | ---------------------- dx = C + ----------------- - log(2 + x) + ------------------------------- | / 2 \ 2 3 | (x + 2)*\x + 3*x + 3/ | /
$$\int \frac{3 x + 5}{\left(x + 2\right) \left(\left(x^{2} + 3 x\right) + 3\right)}\, dx = C - \log{\left(x + 2 \right)} + \frac{\log{\left(x^{2} + 3 x + 3 \right)}}{2} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{3}{2}\right)}{3} \right)}}{3}$$
Gráfica
Respuesta
[src]
/ ___\
___ |5*\/ 3 |
___ 5*\/ 3 *atan|-------|
log(7) 3*log(3) 5*pi*\/ 3 \ 3 /
------ - -------- - ---------- + --------------------- + log(2)
2 2 9 3
$$- \frac{5 \sqrt{3} \pi}{9} - \frac{3 \log{\left(3 \right)}}{2} + \log{\left(2 \right)} + \frac{\log{\left(7 \right)}}{2} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{5 \sqrt{3}}{3} \right)}}{3}$$
=
=
/ ___\
___ |5*\/ 3 |
___ 5*\/ 3 *atan|-------|
log(7) 3*log(3) 5*pi*\/ 3 \ 3 /
------ - -------- - ---------- + --------------------- + log(2)
2 2 9 3
$$- \frac{5 \sqrt{3} \pi}{9} - \frac{3 \log{\left(3 \right)}}{2} + \log{\left(2 \right)} + \frac{\log{\left(7 \right)}}{2} + \frac{5 \sqrt{3} \operatorname{atan}{\left(\frac{5 \sqrt{3}}{3} \right)}}{3}$$
log(7)/2 - 3*log(3)/2 - 5*pi*sqrt(3)/9 + 5*sqrt(3)*atan(5*sqrt(3)/3)/3 + log(2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.