Sr Examen
Integral de 1\(tan^2(x)+1) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------- dx | 2 | tan (x) + 1 | / 0
$$\int\limits_{0}^{1} \frac{1}{\tan^{2}{\left(x \right)} + 1}\, dx$$
Integral(1/(tan(x)^2 + 1), (x, 0, 1))
Respuesta (Indefinida)
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/ | 2 | 1 x tan(x) x*tan (x) | ----------- dx = C + ------------- + ------------- + ------------- | 2 2 2 2 | tan (x) + 1 2 + 2*tan (x) 2 + 2*tan (x) 2 + 2*tan (x) | /
$$\int \frac{1}{\tan^{2}{\left(x \right)} + 1}\, dx = C + \frac{x \tan^{2}{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2} + \frac{x}{2 \tan^{2}{\left(x \right)} + 2} + \frac{\tan{\left(x \right)}}{2 \tan^{2}{\left(x \right)} + 2}$$
Gráfica
Respuesta
[src]
2
1 tan (1) tan(1)
------------- + ------------- + -------------
2 2 2
2 + 2*tan (1) 2 + 2*tan (1) 2 + 2*tan (1)
$$\frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}}$$
=
=
2
1 tan (1) tan(1)
------------- + ------------- + -------------
2 2 2
2 + 2*tan (1) 2 + 2*tan (1) 2 + 2*tan (1)
$$\frac{1}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}} + \frac{\tan^{2}{\left(1 \right)}}{2 + 2 \tan^{2}{\left(1 \right)}}$$
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.