Sr Examen
Integral de cos(3*x)/(x^2+1)^2 dx
Solución
Ha introducido
[src]
oo / | | cos(3*x) | --------- dx | 2 | / 2 \ | \x + 1/ | / -oo
$$\int\limits_{-\infty}^{\infty} \frac{\cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx$$
Integral(cos(3*x)/(x^2 + 1)^2, (x, -oo, oo))
Respuesta (Indefinida)
[src]
/ / | | | cos(3*x) | cos(3*x) | --------- dx = C + | --------- dx | 2 | 2 | / 2 \ | / 2\ | \x + 1/ | \1 + x / | | / /
$$\int \frac{\cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx = C + \int \frac{\cos{\left(3 x \right)}}{\left(x^{2} + 1\right)^{2}}\, dx$$
Gráfica
Respuesta
[src]
____ / ____ / 9*sinh(3) 3*cosh(3)\ ____ / 3*sinh(3) 9*cosh(3)\\
2*\/ pi *|\/ pi *|- --------- + ---------| + \/ pi *|- --------- + ---------||
\ \ 4 4 / \ 4 4 //
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3
$$\frac{2 \sqrt{\pi} \left(\sqrt{\pi} \left(- \frac{9 \sinh{\left(3 \right)}}{4} + \frac{3 \cosh{\left(3 \right)}}{4}\right) + \sqrt{\pi} \left(- \frac{3 \sinh{\left(3 \right)}}{4} + \frac{9 \cosh{\left(3 \right)}}{4}\right)\right)}{3}$$
=
=
____ / ____ / 9*sinh(3) 3*cosh(3)\ ____ / 3*sinh(3) 9*cosh(3)\\
2*\/ pi *|\/ pi *|- --------- + ---------| + \/ pi *|- --------- + ---------||
\ \ 4 4 / \ 4 4 //
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3
$$\frac{2 \sqrt{\pi} \left(\sqrt{\pi} \left(- \frac{9 \sinh{\left(3 \right)}}{4} + \frac{3 \cosh{\left(3 \right)}}{4}\right) + \sqrt{\pi} \left(- \frac{3 \sinh{\left(3 \right)}}{4} + \frac{9 \cosh{\left(3 \right)}}{4}\right)\right)}{3}$$
2*sqrt(pi)*(sqrt(pi)*(-9*sinh(3)/4 + 3*cosh(3)/4) + sqrt(pi)*(-3*sinh(3)/4 + 9*cosh(3)/4))/3
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.