Sr Examen
Integral de arctan(1/(2x^2)) dx
Solución
Ha introducido
[src]
1 / | | / 1 \ | atan|----| dx | | 2| | \2*x / | / 0
$$\int\limits_{0}^{1} \operatorname{atan}{\left(\frac{1}{2 x^{2}} \right)}\, dx$$
Integral(atan(1/(2*x^2)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | / 2\ / 2\ | / 1 \ atan(1 + 2*x) atan(-1 + 2*x) log\1 + 2*x + 2*x / log\1 - 2*x + 2*x / / 1 \ | atan|----| dx = C + ------------- + -------------- - ------------------- + ------------------- + x*atan|----| | | 2| 2 2 4 4 | 2| | \2*x / \2*x / | /
$$\int \operatorname{atan}{\left(\frac{1}{2 x^{2}} \right)}\, dx = C + x \operatorname{atan}{\left(\frac{1}{2 x^{2}} \right)} + \frac{\log{\left(2 x^{2} - 2 x + 1 \right)}}{4} - \frac{\log{\left(2 x^{2} + 2 x + 1 \right)}}{4} + \frac{\operatorname{atan}{\left(2 x - 1 \right)}}{2} + \frac{\operatorname{atan}{\left(2 x + 1 \right)}}{2}$$
Gráfica
Respuesta
[src]
atan(1/2) log(10) log(2)
--------- - ------- + ------ + atan(3)
2 4 4
$$- \frac{\log{\left(10 \right)}}{4} + \frac{\log{\left(2 \right)}}{4} + \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \operatorname{atan}{\left(3 \right)}$$
=
=
atan(1/2) log(10) log(2)
--------- - ------- + ------ + atan(3)
2 4 4
$$- \frac{\log{\left(10 \right)}}{4} + \frac{\log{\left(2 \right)}}{4} + \frac{\operatorname{atan}{\left(\frac{1}{2} \right)}}{2} + \operatorname{atan}{\left(3 \right)}$$
atan(1/2)/2 - log(10)/4 + log(2)/4 + atan(3)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.