Sr Examen
Integral de (sin3x)/(sin^2(3x)+cos^2(3x)) dx
Solución
Ha introducido
[src]
1 / | | sin(3*x) | --------------------- dx | 2 2 | sin (3*x) + cos (3*x) | / 0
$$\int\limits_{0}^{1} \frac{\sin{\left(3 x \right)}}{\sin^{2}{\left(3 x \right)} + \cos^{2}{\left(3 x \right)}}\, dx$$
Integral(sin(3*x)/(sin(3*x)^2 + cos(3*x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | sin(3*x) cos(3*x) | --------------------- dx = C - ------------------------- | 2 2 2 2 | sin (3*x) + cos (3*x) 3*cos (3*x) + 3*sin (3*x) | /
$$\int \frac{\sin{\left(3 x \right)}}{\sin^{2}{\left(3 x \right)} + \cos^{2}{\left(3 x \right)}}\, dx = C - \frac{\cos{\left(3 x \right)}}{3 \sin^{2}{\left(3 x \right)} + 3 \cos^{2}{\left(3 x \right)}}$$
Gráfica
Respuesta
[src]
1 cos(3)
- - ---------------------
3 2 2
3*cos (3) + 3*sin (3)
$$- \frac{\cos{\left(3 \right)}}{3 \sin^{2}{\left(3 \right)} + 3 \cos^{2}{\left(3 \right)}} + \frac{1}{3}$$
=
=
1 cos(3)
- - ---------------------
3 2 2
3*cos (3) + 3*sin (3)
$$- \frac{\cos{\left(3 \right)}}{3 \sin^{2}{\left(3 \right)} + 3 \cos^{2}{\left(3 \right)}} + \frac{1}{3}$$
1/3 - cos(3)/(3*cos(3)^2 + 3*sin(3)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.