Sr Examen
Integral de sqrt(4*x^4+1)/((2*x)) dx
Solución
Ha introducido
[src]
2 / | | __________ | / 4 | \/ 4*x + 1 | ------------- dx | 2*x | / 1
$$\int\limits_{1}^{2} \frac{\sqrt{4 x^{4} + 1}}{2 x}\, dx$$
Integral(sqrt(4*x^4 + 1)/((2*x)), (x, 1, 2))
Respuesta (Indefinida)
[src]
/
| / 1 \
| __________ asinh|----|
| / 4 | 2| 2
| \/ 4*x + 1 \2*x / x 1
| ------------- dx = C - ----------- + ----------------- + --------------------
| 2*x 4 __________ __________
| / 1 2 / 1
/ 2* / 1 + ---- 8*x * / 1 + ----
/ 4 / 4
\/ 4*x \/ 4*x
$$\int \frac{\sqrt{4 x^{4} + 1}}{2 x}\, dx = C + \frac{x^{2}}{2 \sqrt{1 + \frac{1}{4 x^{4}}}} - \frac{\operatorname{asinh}{\left(\frac{1}{2 x^{2}} \right)}}{4} + \frac{1}{8 x^{2} \sqrt{1 + \frac{1}{4 x^{4}}}}$$
Gráfica
Respuesta
[src]
___ ____
\/ 5 asinh(1/8) \/ 65 asinh(1/2)
- ----- - ---------- + ------ + ----------
4 4 4 4
$$- \frac{\sqrt{5}}{4} - \frac{\operatorname{asinh}{\left(\frac{1}{8} \right)}}{4} + \frac{\operatorname{asinh}{\left(\frac{1}{2} \right)}}{4} + \frac{\sqrt{65}}{4}$$
=
=
___ ____
\/ 5 asinh(1/8) \/ 65 asinh(1/2)
- ----- - ---------- + ------ + ----------
4 4 4 4
$$- \frac{\sqrt{5}}{4} - \frac{\operatorname{asinh}{\left(\frac{1}{8} \right)}}{4} + \frac{\operatorname{asinh}{\left(\frac{1}{2} \right)}}{4} + \frac{\sqrt{65}}{4}$$
-sqrt(5)/4 - asinh(1/8)/4 + sqrt(65)/4 + asinh(1/2)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.