Sr Examen
Integral de (3^(arctanx)-x+2)/(x^2-1) dx
Solución
Ha introducido
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1 / | | atan(x) | 3 - x + 2 | ---------------- dx | 2 | x - 1 | / 0
$$\int\limits_{0}^{1} \frac{\left(3^{\operatorname{atan}{\left(x \right)}} - x\right) + 2}{x^{2} - 1}\, dx$$
Integral((3^atan(x) - x + 2)/(x^2 - 1), (x, 0, 1))
Respuesta (Indefinida)
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/ / | | | atan(x) // 2 \ / 2\ | atan(x) | 3 - x + 2 ||-acoth(x) for x > 1| log\-1 + x / | 3 | ---------------- dx = C + 2*|< | - ------------ + | ---------------- dx | 2 || 2 | 2 | (1 + x)*(-1 + x) | x - 1 \\-atanh(x) for x < 1/ | | / /
$$\int \frac{\left(3^{\operatorname{atan}{\left(x \right)}} - x\right) + 2}{x^{2} - 1}\, dx = C + 2 \left(\begin{cases} - \operatorname{acoth}{\left(x \right)} & \text{for}\: x^{2} > 1 \\- \operatorname{atanh}{\left(x \right)} & \text{for}\: x^{2} < 1 \end{cases}\right) - \frac{\log{\left(x^{2} - 1 \right)}}{2} + \int \frac{3^{\operatorname{atan}{\left(x \right)}}}{\left(x - 1\right) \left(x + 1\right)}\, dx$$
Respuesta
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1 / | | atan(x) | 2 + 3 - x | ---------------- dx | (1 + x)*(-1 + x) | / 0
$$\int\limits_{0}^{1} \frac{3^{\operatorname{atan}{\left(x \right)}} - x + 2}{\left(x - 1\right) \left(x + 1\right)}\, dx$$
=
=
1 / | | atan(x) | 2 + 3 - x | ---------------- dx | (1 + x)*(-1 + x) | / 0
$$\int\limits_{0}^{1} \frac{3^{\operatorname{atan}{\left(x \right)}} - x + 2}{\left(x - 1\right) \left(x + 1\right)}\, dx$$
Integral((2 + 3^atan(x) - x)/((1 + x)*(-1 + x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.