Sr Examen
Integral de dx/(x^4+16) dx
Solución
Ha introducido
[src]
1 / | | 1 | ------- dx | 4 | x + 16 | / 0
$$\int\limits_{0}^{1} \frac{1}{x^{4} + 16}\, dx$$
Integral(1/(x^4 + 16), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___\ / ___ | x*\/ 2 | ___ | x*\/ 2 | | ___ / 2 ___\ \/ 2 *atan|1 + -------| \/ 2 *atan|-1 + -------| ___ / 2 ___\ | 1 \/ 2 *log\4 + x - 2*x*\/ 2 / \ 2 / \ 2 / \/ 2 *log\4 + x + 2*x*\/ 2 / | ------- dx = C - ----------------------------- + ----------------------- + ------------------------ + ----------------------------- | 4 64 32 32 64 | x + 16 | /
$$\int \frac{1}{x^{4} + 16}\, dx = C - \frac{\sqrt{2} \log{\left(x^{2} - 2 \sqrt{2} x + 4 \right)}}{64} + \frac{\sqrt{2} \log{\left(x^{2} + 2 \sqrt{2} x + 4 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} - 1 \right)}}{32} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2} x}{2} + 1 \right)}}{32}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ | \/ 2 | ___ | \/ 2 |
\/ 2 *atan|1 - -----| ___ / ___\ \/ 2 *atan|1 + -----| ___ / ___\
\ 2 / \/ 2 *log\5 - 2*\/ 2 / \ 2 / \/ 2 *log\5 + 2*\/ 2 /
- --------------------- - ---------------------- + --------------------- + ----------------------
32 64 32 64
$$- \frac{\sqrt{2} \log{\left(5 - 2 \sqrt{2} \right)}}{64} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{2}}{2} \right)}}{32} + \frac{\sqrt{2} \log{\left(2 \sqrt{2} + 5 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} + 1 \right)}}{32}$$
=
=
/ ___\ / ___\
___ | \/ 2 | ___ | \/ 2 |
\/ 2 *atan|1 - -----| ___ / ___\ \/ 2 *atan|1 + -----| ___ / ___\
\ 2 / \/ 2 *log\5 - 2*\/ 2 / \ 2 / \/ 2 *log\5 + 2*\/ 2 /
- --------------------- - ---------------------- + --------------------- + ----------------------
32 64 32 64
$$- \frac{\sqrt{2} \log{\left(5 - 2 \sqrt{2} \right)}}{64} - \frac{\sqrt{2} \operatorname{atan}{\left(1 - \frac{\sqrt{2}}{2} \right)}}{32} + \frac{\sqrt{2} \log{\left(2 \sqrt{2} + 5 \right)}}{64} + \frac{\sqrt{2} \operatorname{atan}{\left(\frac{\sqrt{2}}{2} + 1 \right)}}{32}$$
-sqrt(2)*atan(1 - sqrt(2)/2)/32 - sqrt(2)*log(5 - 2*sqrt(2))/64 + sqrt(2)*atan(1 + sqrt(2)/2)/32 + sqrt(2)*log(5 + 2*sqrt(2))/64
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.