Sr Examen
Integral de dx/(4+25*x^4) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------- dx | 4 | 4 + 25*x | / 0
$$\int\limits_{0}^{1} \frac{1}{25 x^{4} + 4}\, dx$$
Integral(1/(4 + 25*x^4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ ___\ / ___\ / ___ |2 2 2*x*\/ 5 | ___ |2 2 2*x*\/ 5 | | \/ 5 *log|- + x - ---------| ___ / ___\ ___ / ___\ \/ 5 *log|- + x + ---------| | 1 \5 5 / \/ 5 *atan\1 + x*\/ 5 / \/ 5 *atan\-1 + x*\/ 5 / \5 5 / | --------- dx = C - ----------------------------- + ----------------------- + ------------------------ + ----------------------------- | 4 80 40 40 80 | 4 + 25*x | /
$$\int \frac{1}{25 x^{4} + 4}\, dx = C - \frac{\sqrt{5} \log{\left(x^{2} - \frac{2 \sqrt{5} x}{5} + \frac{2}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(x^{2} + \frac{2 \sqrt{5} x}{5} + \frac{2}{5} \right)}}{80} + \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} x - 1 \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(\sqrt{5} x + 1 \right)}}{40}$$
Gráfica
Respuesta
[src]
/ ___\ / ___\
___ |7 2*\/ 5 | ___ |7 2*\/ 5 |
___ / ___\ \/ 5 *log|- - -------| ___ / ___\ \/ 5 *log|- + -------|
\/ 5 *atan\1 - \/ 5 / \5 5 / \/ 5 *atan\1 + \/ 5 / \5 5 /
- --------------------- - ---------------------- + --------------------- + ----------------------
40 80 40 80
$$- \frac{\sqrt{5} \log{\left(\frac{7}{5} - \frac{2 \sqrt{5}}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(\frac{2 \sqrt{5}}{5} + \frac{7}{5} \right)}}{80} - \frac{\sqrt{5} \operatorname{atan}{\left(1 - \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(1 + \sqrt{5} \right)}}{40}$$
=
=
/ ___\ / ___\
___ |7 2*\/ 5 | ___ |7 2*\/ 5 |
___ / ___\ \/ 5 *log|- - -------| ___ / ___\ \/ 5 *log|- + -------|
\/ 5 *atan\1 - \/ 5 / \5 5 / \/ 5 *atan\1 + \/ 5 / \5 5 /
- --------------------- - ---------------------- + --------------------- + ----------------------
40 80 40 80
$$- \frac{\sqrt{5} \log{\left(\frac{7}{5} - \frac{2 \sqrt{5}}{5} \right)}}{80} + \frac{\sqrt{5} \log{\left(\frac{2 \sqrt{5}}{5} + \frac{7}{5} \right)}}{80} - \frac{\sqrt{5} \operatorname{atan}{\left(1 - \sqrt{5} \right)}}{40} + \frac{\sqrt{5} \operatorname{atan}{\left(1 + \sqrt{5} \right)}}{40}$$
-sqrt(5)*atan(1 - sqrt(5))/40 - sqrt(5)*log(7/5 - 2*sqrt(5)/5)/80 + sqrt(5)*atan(1 + sqrt(5))/40 + sqrt(5)*log(7/5 + 2*sqrt(5)/5)/80
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.