Sr Examen
Integral de (tgxdx)/(2tg^2x+11) dx
Solución
Ha introducido
[src]
1 / | | tan(x) | -------------- dx | 2 | 2*tan (x) + 11 | / 0
$$\int\limits_{0}^{1} \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 11}\, dx$$
Integral(tan(x)/(2*tan(x)^2 + 11), (x, 0, 1))
Respuesta (Indefinida)
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/ | / 2 \ / 2 \ | tan(x) log\22 + 4*tan (x)/ log\4 + 4*tan (x)/ | -------------- dx = C - ------------------- + ------------------ | 2 18 18 | 2*tan (x) + 11 | /
$$\int \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 11}\, dx = C + \frac{\log{\left(4 \tan^{2}{\left(x \right)} + 4 \right)}}{18} - \frac{\log{\left(4 \tan^{2}{\left(x \right)} + 22 \right)}}{18}$$
Gráfica
Respuesta
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/ 2 \ / 2 \
log\11 + 2*tan (1)/ log(11) log\1 + tan (1)/
- ------------------- + ------- + ----------------
18 18 18
$$- \frac{\log{\left(2 \tan^{2}{\left(1 \right)} + 11 \right)}}{18} + \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{18} + \frac{\log{\left(11 \right)}}{18}$$
=
=
/ 2 \ / 2 \
log\11 + 2*tan (1)/ log(11) log\1 + tan (1)/
- ------------------- + ------- + ----------------
18 18 18
$$- \frac{\log{\left(2 \tan^{2}{\left(1 \right)} + 11 \right)}}{18} + \frac{\log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{18} + \frac{\log{\left(11 \right)}}{18}$$
-log(11 + 2*tan(1)^2)/18 + log(11)/18 + log(1 + tan(1)^2)/18
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.