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