Sr Examen
Integral de (x-3)/((x+2)(x^2+5)) dx
Solución
Ha introducido
[src]
1 / | | x - 3 | ---------------- dx | / 2 \ | (x + 2)*\x + 5/ | / 0
$$\int\limits_{0}^{1} \frac{x - 3}{\left(x + 2\right) \left(x^{2} + 5\right)}\, dx$$
Integral((x - 3)/(((x + 2)*(x^2 + 5))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___ |x*\/ 5 | | / 2\ \/ 5 *atan|-------| | x - 3 5*log(2 + x) 5*log\5 + x / \ 5 / | ---------------- dx = C - ------------ + ------------- - ------------------- | / 2 \ 9 18 45 | (x + 2)*\x + 5/ | /
$$\int \frac{x - 3}{\left(x + 2\right) \left(x^{2} + 5\right)}\, dx = C - \frac{5 \log{\left(x + 2 \right)}}{9} + \frac{5 \log{\left(x^{2} + 5 \right)}}{18} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5} x}{5} \right)}}{45}$$
Gráfica
Respuesta
[src]
/ ___\
___ |\/ 5 |
\/ 5 *atan|-----|
5*log(3) 5*log(5) 5*log(2) 5*log(6) \ 5 /
- -------- - -------- + -------- + -------- - -----------------
9 18 9 18 45
$$- \frac{5 \log{\left(3 \right)}}{9} - \frac{5 \log{\left(5 \right)}}{18} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} \right)}}{45} + \frac{5 \log{\left(2 \right)}}{9} + \frac{5 \log{\left(6 \right)}}{18}$$
=
=
/ ___\
___ |\/ 5 |
\/ 5 *atan|-----|
5*log(3) 5*log(5) 5*log(2) 5*log(6) \ 5 /
- -------- - -------- + -------- + -------- - -----------------
9 18 9 18 45
$$- \frac{5 \log{\left(3 \right)}}{9} - \frac{5 \log{\left(5 \right)}}{18} - \frac{\sqrt{5} \operatorname{atan}{\left(\frac{\sqrt{5}}{5} \right)}}{45} + \frac{5 \log{\left(2 \right)}}{9} + \frac{5 \log{\left(6 \right)}}{18}$$
-5*log(3)/9 - 5*log(5)/18 + 5*log(2)/9 + 5*log(6)/18 - sqrt(5)*atan(sqrt(5)/5)/45
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.