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