Sr Examen
Integral de 1/(x⁴+1) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------ dx | 4 | x + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{4} + 1}\, dx$$
Integral(1/(x^4 + 1), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | ___ / 2 ___\ ___ / ___\ ___ / ___\ ___ / 2 ___\ | 1 \/ 2 *log\1 + x - x*\/ 2 / \/ 2 *atan\1 + x*\/ 2 / \/ 2 *atan\-1 + x*\/ 2 / \/ 2 *log\1 + x + x*\/ 2 / | ------ dx = C - --------------------------- + ----------------------- + ------------------------ + --------------------------- | 4 8 4 4 8 | x + 1 | /
$$\int \frac{1}{x^{4} + 1}\, dx = C - \frac{\sqrt{2} \log{\left(x^{2} - \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \log{\left(x^{2} + \sqrt{2} x + 1 \right)}}{8} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x - 1 \right)}}{4} + \frac{\sqrt{2} \operatorname{atan}{\left(\sqrt{2} x + 1 \right)}}{4}$$
Gráfica
Respuesta
[src]
___ / ___\ ___ ___ / ___\
\/ 2 *log\2 - \/ 2 / pi*\/ 2 \/ 2 *log\2 + \/ 2 /
- -------------------- + -------- + --------------------
8 8 8
$$- \frac{\sqrt{2} \log{\left(2 - \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \pi}{8}$$
=
=
___ / ___\ ___ ___ / ___\
\/ 2 *log\2 - \/ 2 / pi*\/ 2 \/ 2 *log\2 + \/ 2 /
- -------------------- + -------- + --------------------
8 8 8
$$- \frac{\sqrt{2} \log{\left(2 - \sqrt{2} \right)}}{8} + \frac{\sqrt{2} \log{\left(\sqrt{2} + 2 \right)}}{8} + \frac{\sqrt{2} \pi}{8}$$
-sqrt(2)*log(2 - sqrt(2))/8 + pi*sqrt(2)/8 + sqrt(2)*log(2 + sqrt(2))/8
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.