Sr Examen
Integral de 1/(3sin4x+2cos4x+2) dx
Solución
Ha introducido
[src]
1 / | | 1 | --------------------------- dx | 3*sin(4*x) + 2*cos(4*x) + 2 | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(3 \sin{\left(4 x \right)} + 2 \cos{\left(4 x \right)}\right) + 2}\, dx$$
Integral(1/(3*sin(4*x) + 2*cos(4*x) + 2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 1 log(2/3 + tan(2*x)) | --------------------------- dx = C + ------------------- | 3*sin(4*x) + 2*cos(4*x) + 2 12 | /
$$\int \frac{1}{\left(3 \sin{\left(4 x \right)} + 2 \cos{\left(4 x \right)}\right) + 2}\, dx = C + \frac{\log{\left(\tan{\left(2 x \right)} + \frac{2}{3} \right)}}{12}$$
Gráfica
Respuesta
[src]
log(2/3) log(-2/3 - tan(2)) pi*I
- -------- + ------------------ + ----
12 12 12
$$- \frac{\log{\left(\frac{2}{3} \right)}}{12} + \frac{\log{\left(- \frac{2}{3} - \tan{\left(2 \right)} \right)}}{12} + \frac{i \pi}{12}$$
=
=
log(2/3) log(-2/3 - tan(2)) pi*I
- -------- + ------------------ + ----
12 12 12
$$- \frac{\log{\left(\frac{2}{3} \right)}}{12} + \frac{\log{\left(- \frac{2}{3} - \tan{\left(2 \right)} \right)}}{12} + \frac{i \pi}{12}$$
-log(2/3)/12 + log(-2/3 - tan(2))/12 + pi*i/12
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.