Sr Examen
Integral de dx*sin(3*x)/x^2 dx
Solución
Ha introducido
[src]
oo / | | sin(3*x) | -------- dx | 2 | x | / 1
$$\int\limits_{1}^{\infty} \frac{\sin{\left(3 x \right)}}{x^{2}}\, dx$$
Integral(sin(3*x)/x^2, (x, 1, oo))
Respuesta (Indefinida)
[src]
/ / | | | sin(3*x) | sin(3*x) | -------- dx = C + | -------- dx | 2 | 2 | x | x | | / /
$$\int \frac{\sin{\left(3 x \right)}}{x^{2}}\, dx = C + \int \frac{\sin{\left(3 x \right)}}{x^{2}}\, dx$$
Respuesta
[src]
| / / pi*I\ \|
| | | ----| ||
| | | 2 | ||
| | 9 9*Ci(3) 3*sin(3) 9*EulerGamma 9*log\3*e / 9*pi*I||
| 4*|- - - ------- + -------- + ------------ + -------------- - ------||
____ | 6 6*EulerGamma 6*log(2) 3*log(9/4) \ 2 2 2 2 2 4 /|
-\/ pi *|------ - ------------ - -------- - ---------- + ---------------------------------------------------------------------|
| ____ ____ ____ ____ ____ |
|\/ pi \/ pi \/ pi \/ pi 3*\/ pi |
--------------------------------------------------------------------------------------------------------------------------------
2
$$- \frac{\sqrt{\pi} \left|{- \frac{6 \log{\left(2 \right)}}{\sqrt{\pi}} - \frac{6 \gamma}{\sqrt{\pi}} - \frac{3 \log{\left(\frac{9}{4} \right)}}{\sqrt{\pi}} + \frac{6}{\sqrt{\pi}} + \frac{4 \left(- \frac{9}{2} - \frac{9 \operatorname{Ci}{\left(3 \right)}}{2} + \frac{3 \sin{\left(3 \right)}}{2} + \frac{9 \gamma}{2} - \frac{9 i \pi}{4} + \frac{9 \log{\left(3 e^{\frac{i \pi}{2}} \right)}}{2}\right)}{3 \sqrt{\pi}}}\right|}{2}$$
=
=
| / / pi*I\ \|
| | | ----| ||
| | | 2 | ||
| | 9 9*Ci(3) 3*sin(3) 9*EulerGamma 9*log\3*e / 9*pi*I||
| 4*|- - - ------- + -------- + ------------ + -------------- - ------||
____ | 6 6*EulerGamma 6*log(2) 3*log(9/4) \ 2 2 2 2 2 4 /|
-\/ pi *|------ - ------------ - -------- - ---------- + ---------------------------------------------------------------------|
| ____ ____ ____ ____ ____ |
|\/ pi \/ pi \/ pi \/ pi 3*\/ pi |
--------------------------------------------------------------------------------------------------------------------------------
2
$$- \frac{\sqrt{\pi} \left|{- \frac{6 \log{\left(2 \right)}}{\sqrt{\pi}} - \frac{6 \gamma}{\sqrt{\pi}} - \frac{3 \log{\left(\frac{9}{4} \right)}}{\sqrt{\pi}} + \frac{6}{\sqrt{\pi}} + \frac{4 \left(- \frac{9}{2} - \frac{9 \operatorname{Ci}{\left(3 \right)}}{2} + \frac{3 \sin{\left(3 \right)}}{2} + \frac{9 \gamma}{2} - \frac{9 i \pi}{4} + \frac{9 \log{\left(3 e^{\frac{i \pi}{2}} \right)}}{2}\right)}{3 \sqrt{\pi}}}\right|}{2}$$
-sqrt(pi)*Abs(6/sqrt(pi) - 6*EulerGamma/sqrt(pi) - 6*log(2)/sqrt(pi) - 3*log(9/4)/sqrt(pi) + 4*(-9/2 - 9*Ci(3)/2 + 3*sin(3)/2 + 9*EulerGamma/2 + 9*log(3*exp_polar(pi*i/2))/2 - 9*pi*i/4)/(3*sqrt(pi)))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.