Sr Examen
Integral de sin(x)/(x^2) dx
Solución
Ha introducido
[src]
oo / | | sin(x) | ------ dx | 2 | x | / pi -- 2
$$\int\limits_{\frac{\pi}{2}}^{\infty} \frac{\sin{\left(x \right)}}{x^{2}}\, dx$$
Integral(sin(x)/x^2, (x, pi/2, oo))
Respuesta (Indefinida)
[src]
/ / | | | sin(x) | sin(x) | ------ dx = C + | ------ dx | 2 | 2 | x | x | | / /
$$\int \frac{\sin{\left(x \right)}}{x^{2}}\, dx = C + \int \frac{\sin{\left(x \right)}}{x^{2}}\, dx$$
Respuesta
[src]
| / / / pi*I\ \ / / 2\\ / / 2\\ / 2\\|
| | | | ----| | | | 3*pi || | | 3*pi || | 3*pi |||
| | | | 2 | | | 256*|6 + -----|| | 256*|6 + -----|| 128*|6 + -----|||
| / 2\ 5/2 | 96 768 | |pi*e | pi*I /pi\| | 48 1536 \ 8 /| | 1536 48 \ 8 /| \ 8 /||
| ____ |pi | pi *|--- + --- + |- log|--------| + ---- + Ci|--||*|--- + ---- - ---------------| + |- ---- - --- + ---------------|*EulerGamma - ---------------||
| \/ pi *log|---| | 3 4 \ \ 2 / 2 \2 // | 2 4 4 | | 4 2 4 | 4 ||
| ____ ____ ____ \ 16/ \pi pi \pi pi pi / \ pi pi pi / pi /|
|\/ pi - \/ pi *EulerGamma - \/ pi *log(2) - --------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------|
| 2 48 |
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
____
\/ pi
$$\frac{\left|{- \sqrt{\pi} \log{\left(2 \right)} - \gamma \sqrt{\pi} - \frac{\sqrt{\pi} \log{\left(\frac{\pi^{2}}{16} \right)}}{2} + \sqrt{\pi} + \frac{\pi^{\frac{5}{2}} \left(- \frac{128 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}} + \gamma \left(- \frac{1536}{\pi^{4}} - \frac{48}{\pi^{2}} + \frac{256 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}}\right) + \frac{96}{\pi^{3}} + \frac{768}{\pi^{4}} + \left(- \frac{256 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}} + \frac{48}{\pi^{2}} + \frac{1536}{\pi^{4}}\right) \left(\operatorname{Ci}{\left(\frac{\pi}{2} \right)} - \log{\left(\frac{\pi e^{\frac{i \pi}{2}}}{2} \right)} + \frac{i \pi}{2}\right)\right)}{48}}\right|}{\sqrt{\pi}}$$
=
=
| / / / pi*I\ \ / / 2\\ / / 2\\ / 2\\|
| | | | ----| | | | 3*pi || | | 3*pi || | 3*pi |||
| | | | 2 | | | 256*|6 + -----|| | 256*|6 + -----|| 128*|6 + -----|||
| / 2\ 5/2 | 96 768 | |pi*e | pi*I /pi\| | 48 1536 \ 8 /| | 1536 48 \ 8 /| \ 8 /||
| ____ |pi | pi *|--- + --- + |- log|--------| + ---- + Ci|--||*|--- + ---- - ---------------| + |- ---- - --- + ---------------|*EulerGamma - ---------------||
| \/ pi *log|---| | 3 4 \ \ 2 / 2 \2 // | 2 4 4 | | 4 2 4 | 4 ||
| ____ ____ ____ \ 16/ \pi pi \pi pi pi / \ pi pi pi / pi /|
|\/ pi - \/ pi *EulerGamma - \/ pi *log(2) - --------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------|
| 2 48 |
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
____
\/ pi
$$\frac{\left|{- \sqrt{\pi} \log{\left(2 \right)} - \gamma \sqrt{\pi} - \frac{\sqrt{\pi} \log{\left(\frac{\pi^{2}}{16} \right)}}{2} + \sqrt{\pi} + \frac{\pi^{\frac{5}{2}} \left(- \frac{128 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}} + \gamma \left(- \frac{1536}{\pi^{4}} - \frac{48}{\pi^{2}} + \frac{256 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}}\right) + \frac{96}{\pi^{3}} + \frac{768}{\pi^{4}} + \left(- \frac{256 \left(\frac{3 \pi^{2}}{8} + 6\right)}{\pi^{4}} + \frac{48}{\pi^{2}} + \frac{1536}{\pi^{4}}\right) \left(\operatorname{Ci}{\left(\frac{\pi}{2} \right)} - \log{\left(\frac{\pi e^{\frac{i \pi}{2}}}{2} \right)} + \frac{i \pi}{2}\right)\right)}{48}}\right|}{\sqrt{\pi}}$$
Abs(sqrt(pi) - sqrt(pi)*EulerGamma - sqrt(pi)*log(2) - sqrt(pi)*log(pi^2/16)/2 + pi^(5/2)*(96/pi^3 + 768/pi^4 + (-log(pi*exp_polar(pi*i/2)/2) + pi*i/2 + Ci(pi/2))*(48/pi^2 + 1536/pi^4 - 256*(6 + 3*pi^2/8)/pi^4) + (-1536/pi^4 - 48/pi^2 + 256*(6 + 3*pi^2/8)/pi^4)*EulerGamma - 128*(6 + 3*pi^2/8)/pi^4)/48)/sqrt(pi)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.