Sr Examen
Integral de (x²+x)/(x^6+1) dx
Solución
Ha introducido
[src]
1 / | | 2 | x + x | ------ dx | 6 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{x^{2} + x}{x^{6} + 1}\, dx$$
Integral((x^2 + x)/(x^6 + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___ / 1 2\\ / |2*\/ 3 *|- - + x || | ___ | \ 2 /| | 2 / 4 2\ / 3\ / 2\ \/ 3 *atan|------------------| | x + x log\1 + x - x / atan\x / log\1 + x / \ 3 / | ------ dx = C - ---------------- + -------- + ----------- + ------------------------------ | 6 12 3 6 6 | x + 1 | /
$$\int \frac{x^{2} + x}{x^{6} + 1}\, dx = C + \frac{\log{\left(x^{2} + 1 \right)}}{6} - \frac{\log{\left(x^{4} - x^{2} + 1 \right)}}{12} + \frac{\operatorname{atan}{\left(x^{3} \right)}}{3} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x^{2} - \frac{1}{2}\right)}{3} \right)}}{6}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
|1 \/ 3 | |1 \/ 3 |
/ ___\ / ___\ pi*|- - -----| 5*pi*|- + -----|
pi log\2 + \/ 3 / log\2 - \/ 3 / log(2) \6 12 / \6 12 /
- -- - -------------- - -------------- + ------ + -------------- + ----------------
12 12 12 6 6 6
$$- \frac{\pi}{12} - \frac{\log{\left(\sqrt{3} + 2 \right)}}{12} + \frac{\pi \left(\frac{1}{6} - \frac{\sqrt{3}}{12}\right)}{6} - \frac{\log{\left(2 - \sqrt{3} \right)}}{12} + \frac{\log{\left(2 \right)}}{6} + \frac{5 \pi \left(\frac{\sqrt{3}}{12} + \frac{1}{6}\right)}{6}$$
=
=
/ ___\ / ___\
|1 \/ 3 | |1 \/ 3 |
/ ___\ / ___\ pi*|- - -----| 5*pi*|- + -----|
pi log\2 + \/ 3 / log\2 - \/ 3 / log(2) \6 12 / \6 12 /
- -- - -------------- - -------------- + ------ + -------------- + ----------------
12 12 12 6 6 6
$$- \frac{\pi}{12} - \frac{\log{\left(\sqrt{3} + 2 \right)}}{12} + \frac{\pi \left(\frac{1}{6} - \frac{\sqrt{3}}{12}\right)}{6} - \frac{\log{\left(2 - \sqrt{3} \right)}}{12} + \frac{\log{\left(2 \right)}}{6} + \frac{5 \pi \left(\frac{\sqrt{3}}{12} + \frac{1}{6}\right)}{6}$$
-pi/12 - log(2 + sqrt(3))/12 - log(2 - sqrt(3))/12 + log(2)/6 + pi*(1/6 - sqrt(3)/12)/6 + 5*pi*(1/6 + sqrt(3)/12)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.