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