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