Sr Examen
Integral de ((sinx)^2)/(x^4) dx
Solución
Ha introducido
[src]
oo / | | 2 | sin (x) | ------- dx | 4 | x | / 1
$$\int\limits_{1}^{\infty} \frac{\sin^{2}{\left(x \right)}}{x^{4}}\, dx$$
Integral(sin(x)^2/x^4, (x, 1, oo))
Respuesta (Indefinida)
[src]
/ | | 2 | sin (x) 2*Si(2*x) 1 cos(2*x) sin(2*x) cos(2*x) | ------- dx = C - --------- - ---- - -------- - -------- + -------- | 4 3 3 3*x 2 3 | x 6*x 6*x 6*x | /
$$\int \frac{\sin^{2}{\left(x \right)}}{x^{4}}\, dx = C - \frac{2 \operatorname{Si}{\left(2 x \right)}}{3} - \frac{\cos{\left(2 x \right)}}{3 x} - \frac{\sin{\left(2 x \right)}}{6 x^{2}} + \frac{\cos{\left(2 x \right)}}{6 x^{3}} - \frac{1}{6 x^{3}}$$
Respuesta
[src]
/ 2 2*cos(2) 2*sin(2) 8*Si(2)\
| ____ - + -------- + -------- + -------|
____ | 4*\/ pi 3 3 3 3 |
\/ pi *|- -------- + ---------------------------------|
| 3 ____ |
\ \/ pi /
-------------------------------------------------------
4
$$\frac{\sqrt{\pi} \left(- \frac{4 \sqrt{\pi}}{3} + \frac{\frac{2 \cos{\left(2 \right)}}{3} + \frac{2 \sin{\left(2 \right)}}{3} + \frac{2}{3} + \frac{8 \operatorname{Si}{\left(2 \right)}}{3}}{\sqrt{\pi}}\right)}{4}$$
=
=
/ 2 2*cos(2) 2*sin(2) 8*Si(2)\
| ____ - + -------- + -------- + -------|
____ | 4*\/ pi 3 3 3 3 |
\/ pi *|- -------- + ---------------------------------|
| 3 ____ |
\ \/ pi /
-------------------------------------------------------
4
$$\frac{\sqrt{\pi} \left(- \frac{4 \sqrt{\pi}}{3} + \frac{\frac{2 \cos{\left(2 \right)}}{3} + \frac{2 \sin{\left(2 \right)}}{3} + \frac{2}{3} + \frac{8 \operatorname{Si}{\left(2 \right)}}{3}}{\sqrt{\pi}}\right)}{4}$$
sqrt(pi)*(-4*sqrt(pi)/3 + (2/3 + 2*cos(2)/3 + 2*sin(2)/3 + 8*Si(2)/3)/sqrt(pi))/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.