Sr Examen
Integral de x/(((x+6)^2)(x^2+X+14)) dx
Solución
Ha introducido
[src]
1 / | | x | ---------------------- dx | 2 / 2 \ | (x + 6) *\x + x + 14/ | / 0
$$\int\limits_{0}^{1} \frac{x}{\left(x + 6\right)^{2} \left(\left(x^{2} + x\right) + 14\right)}\, dx$$
Integral(x/(((x + 6)^2*(x^2 + x + 14))), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ____ \ / ____ |2*\/ 55 *(1/2 + x)| | / 2\ 13*\/ 55 *atan|------------------| | x log(6 + x) log\14 + x + x / 3 \ 55 / | ---------------------- dx = C - ---------- + ---------------- + ---------- + ---------------------------------- | 2 / 2 \ 88 176 22*(6 + x) 4840 | (x + 6) *\x + x + 14/ | /
$$\int \frac{x}{\left(x + 6\right)^{2} \left(\left(x^{2} + x\right) + 14\right)}\, dx = C - \frac{\log{\left(x + 6 \right)}}{88} + \frac{\log{\left(x^{2} + x + 14 \right)}}{176} + \frac{13 \sqrt{55} \operatorname{atan}{\left(\frac{2 \sqrt{55} \left(x + \frac{1}{2}\right)}{55} \right)}}{4840} + \frac{3}{22 \left(x + 6\right)}$$
Gráfica
Respuesta
[src]
/ ____\ / ____\
____ |\/ 55 | ____ |3*\/ 55 |
13*\/ 55 *atan|------| 13*\/ 55 *atan|--------|
1 log(7) log(14) log(6) log(16) \ 55 / \ 55 /
- --- - ------ - ------- + ------ + ------- - ---------------------- + ------------------------
308 88 176 88 176 4840 4840
$$- \frac{\log{\left(7 \right)}}{88} - \frac{\log{\left(14 \right)}}{176} - \frac{1}{308} - \frac{13 \sqrt{55} \operatorname{atan}{\left(\frac{\sqrt{55}}{55} \right)}}{4840} + \frac{13 \sqrt{55} \operatorname{atan}{\left(\frac{3 \sqrt{55}}{55} \right)}}{4840} + \frac{\log{\left(16 \right)}}{176} + \frac{\log{\left(6 \right)}}{88}$$
=
=
/ ____\ / ____\
____ |\/ 55 | ____ |3*\/ 55 |
13*\/ 55 *atan|------| 13*\/ 55 *atan|--------|
1 log(7) log(14) log(6) log(16) \ 55 / \ 55 /
- --- - ------ - ------- + ------ + ------- - ---------------------- + ------------------------
308 88 176 88 176 4840 4840
$$- \frac{\log{\left(7 \right)}}{88} - \frac{\log{\left(14 \right)}}{176} - \frac{1}{308} - \frac{13 \sqrt{55} \operatorname{atan}{\left(\frac{\sqrt{55}}{55} \right)}}{4840} + \frac{13 \sqrt{55} \operatorname{atan}{\left(\frac{3 \sqrt{55}}{55} \right)}}{4840} + \frac{\log{\left(16 \right)}}{176} + \frac{\log{\left(6 \right)}}{88}$$
-1/308 - log(7)/88 - log(14)/176 + log(6)/88 + log(16)/176 - 13*sqrt(55)*atan(sqrt(55)/55)/4840 + 13*sqrt(55)*atan(3*sqrt(55)/55)/4840
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.