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