Sr Examen
Integral de tg(x)/(tg(x)^2+4*tg(x)+4) dx
Solución
Ha introducido
[src]
1 / | | tan(x) | ---------------------- dx | 2 | tan (x) + 4*tan(x) + 4 | / 0
$$\int\limits_{0}^{1} \frac{\tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)}\right) + 4}\, dx$$
Integral(tan(x)/(tan(x)^2 + 4*tan(x) + 4), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | / 2 \ / 2 \ | tan(x) 20 12*log(2 + tan(x)) 6*log\1 + tan (x)/ 16*x 6*log(2 + tan(x))*tan(x) 3*log\1 + tan (x)/*tan(x) 8*x*tan(x) | ---------------------- dx = C + --------------- - ------------------ + ------------------ + --------------- - ------------------------ + ------------------------- + --------------- | 2 100 + 50*tan(x) 100 + 50*tan(x) 100 + 50*tan(x) 100 + 50*tan(x) 100 + 50*tan(x) 100 + 50*tan(x) 100 + 50*tan(x) | tan (x) + 4*tan(x) + 4 | /
$$\int \frac{\tan{\left(x \right)}}{\left(\tan^{2}{\left(x \right)} + 4 \tan{\left(x \right)}\right) + 4}\, dx = C + \frac{8 x \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{16 x}{50 \tan{\left(x \right)} + 100} - \frac{6 \log{\left(\tan{\left(x \right)} + 2 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} - \frac{12 \log{\left(\tan{\left(x \right)} + 2 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{3 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)} \tan{\left(x \right)}}{50 \tan{\left(x \right)} + 100} + \frac{6 \log{\left(\tan^{2}{\left(x \right)} + 1 \right)}}{50 \tan{\left(x \right)} + 100} + \frac{20}{50 \tan{\left(x \right)} + 100}$$
Gráfica
Respuesta
[src]
/ 2 \ / 2 \ 1 36 3*log(2) 12*log(2 + tan(1)) 6*log\1 + tan (1)/ 8*tan(1) 6*log(2 + tan(1))*tan(1) 3*log\1 + tan (1)/*tan(1) - - + --------------- + -------- - ------------------ + ------------------ + --------------- - ------------------------ + ------------------------- 5 100 + 50*tan(1) 25 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1)
$$- \frac{1}{5} - \frac{12 \log{\left(\tan{\left(1 \right)} + 2 \right)}}{50 \tan{\left(1 \right)} + 100} - \frac{6 \log{\left(\tan{\left(1 \right)} + 2 \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{6 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{8 \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(2 \right)}}{25} + \frac{36}{50 \tan{\left(1 \right)} + 100}$$
=
=
/ 2 \ / 2 \ 1 36 3*log(2) 12*log(2 + tan(1)) 6*log\1 + tan (1)/ 8*tan(1) 6*log(2 + tan(1))*tan(1) 3*log\1 + tan (1)/*tan(1) - - + --------------- + -------- - ------------------ + ------------------ + --------------- - ------------------------ + ------------------------- 5 100 + 50*tan(1) 25 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1) 100 + 50*tan(1)
$$- \frac{1}{5} - \frac{12 \log{\left(\tan{\left(1 \right)} + 2 \right)}}{50 \tan{\left(1 \right)} + 100} - \frac{6 \log{\left(\tan{\left(1 \right)} + 2 \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)} \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{6 \log{\left(1 + \tan^{2}{\left(1 \right)} \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{8 \tan{\left(1 \right)}}{50 \tan{\left(1 \right)} + 100} + \frac{3 \log{\left(2 \right)}}{25} + \frac{36}{50 \tan{\left(1 \right)} + 100}$$
-1/5 + 36/(100 + 50*tan(1)) + 3*log(2)/25 - 12*log(2 + tan(1))/(100 + 50*tan(1)) + 6*log(1 + tan(1)^2)/(100 + 50*tan(1)) + 8*tan(1)/(100 + 50*tan(1)) - 6*log(2 + tan(1))*tan(1)/(100 + 50*tan(1)) + 3*log(1 + tan(1)^2)*tan(1)/(100 + 50*tan(1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.