Sr Examen
Integral de x^2/(xsinx+xcosx)^2 dx
Solución
Ha introducido
[src]
pi / | | 2 | x | ---------------------- dx | 2 | (x*sin(x) + x*cos(x)) | / 0
$$\int\limits_{0}^{\pi} \frac{x^{2}}{\left(x \sin{\left(x \right)} + x \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral(x^2/(x*sin(x) + x*cos(x))^2, (x, 0, pi))
Respuesta (Indefinida)
[src]
/ | /x\ | 2 2*tan|-| | x \2/ | ---------------------- dx = C - ----------------------- | 2 2/x\ /x\ | (x*sin(x) + x*cos(x)) -1 + tan |-| - 2*tan|-| | \2/ \2/ /
$$\int \frac{x^{2}}{\left(x \sin{\left(x \right)} + x \cos{\left(x \right)}\right)^{2}}\, dx = C - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)} - 1}$$
Gráfica
Respuesta
[src]
pi / | | 2 | x | ---------------------- dx | 2 | (x*cos(x) + x*sin(x)) | / 0
$$\int\limits_{0}^{\pi} \frac{x^{2}}{\left(x \sin{\left(x \right)} + x \cos{\left(x \right)}\right)^{2}}\, dx$$
=
=
pi / | | 2 | x | ---------------------- dx | 2 | (x*cos(x) + x*sin(x)) | / 0
$$\int\limits_{0}^{\pi} \frac{x^{2}}{\left(x \sin{\left(x \right)} + x \cos{\left(x \right)}\right)^{2}}\, dx$$
Integral(x^2/(x*cos(x) + x*sin(x))^2, (x, 0, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.