Sr Examen
Integral de (tg(x))/(1+4tg^2(x)) dx
Solución
Ha introducido
[src]
1 / | | tan(x) | ------------- dx | 2 | 1 + 4*tan (x) | / 0
$$\int\limits_{0}^{1} \frac{\tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} + 1}\, dx$$
Integral(tan(x)/(1 + 4*tan(x)^2), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | / 2 \ / 2 \ | tan(x) log\8 + 8*tan (x)/ log\2 + 8*tan (x)/ | ------------- dx = C - ------------------ + ------------------ | 2 6 6 | 1 + 4*tan (x) | /
$$\int \frac{\tan{\left(x \right)}}{4 \tan^{2}{\left(x \right)} + 1}\, dx = C + \frac{\log{\left(8 \tan^{2}{\left(x \right)} + 2 \right)}}{6} - \frac{\log{\left(8 \tan^{2}{\left(x \right)} + 8 \right)}}{6}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \
log\1 + tan (1)/ log\1 + 4*tan (1)/
- ---------------- + ------------------
6 6
$$- \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{6} + \frac{\log{\left(1 + 4 \tan^{2}{\left(1 \right)} \right)}}{6}$$
=
=
/ 2 \ / 2 \
log\1 + tan (1)/ log\1 + 4*tan (1)/
- ---------------- + ------------------
6 6
$$- \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{6} + \frac{\log{\left(1 + 4 \tan^{2}{\left(1 \right)} \right)}}{6}$$
-log(1 + tan(1)^2)/6 + log(1 + 4*tan(1)^2)/6
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.