Sr Examen
Integral de log(e)(1+sqrt(x^2+y^2))/sqrt(x^2+y^2) dx
Solución
Ha introducido
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1 / | | / _________\ | | / 2 2 | | log(E)*\1 + \/ x + y / | ------------------------- dx | _________ | / 2 2 | \/ x + y | / 0
$$\int\limits_{0}^{1} \frac{\left(\sqrt{x^{2} + y^{2}} + 1\right) \log{\left(e \right)}}{\sqrt{x^{2} + y^{2}}}\, dx$$
Integral((log(E)*(1 + sqrt(x^2 + y^2)))/sqrt(x^2 + y^2), (x, 0, 1))
Respuesta (Indefinida)
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/ // / ____\ \ | || | / 1 | 2 | | / _________\ ||asinh|x* / -- | for y > 0| | | / 2 2 | || | / 2 | | | log(E)*\1 + \/ x + y / || \ \/ y / | | ------------------------- dx = C + x + |< | | _________ || / _____\ | | / 2 2 || | / -1 | 2 | | \/ x + y ||acosh|x* / --- | for y < 0| | || | / 2 | | / \\ \ \/ y / /
$$\int \frac{\left(\sqrt{x^{2} + y^{2}} + 1\right) \log{\left(e \right)}}{\sqrt{x^{2} + y^{2}}}\, dx = C + x + \begin{cases} \operatorname{asinh}{\left(x \sqrt{\frac{1}{y^{2}}} \right)} & \text{for}\: y^{2} > 0 \\\operatorname{acosh}{\left(x \sqrt{- \frac{1}{y^{2}}} \right)} & \text{for}\: y^{2} < 0 \end{cases}$$
Respuesta
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// / ____\ \
|| | / 1 | |
||asinh| / -- | for And(y > -oo, y < oo, y != 0)|
1 + |< | / 2 | |
|| \\/ y / |
|| |
\\ nan otherwise /
$$\begin{cases} \operatorname{asinh}{\left(\sqrt{\frac{1}{y^{2}}} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\\text{NaN} & \text{otherwise} \end{cases} + 1$$
=
=
// / ____\ \
|| | / 1 | |
||asinh| / -- | for And(y > -oo, y < oo, y != 0)|
1 + |< | / 2 | |
|| \\/ y / |
|| |
\\ nan otherwise /
$$\begin{cases} \operatorname{asinh}{\left(\sqrt{\frac{1}{y^{2}}} \right)} & \text{for}\: y > -\infty \wedge y < \infty \wedge y \neq 0 \\\text{NaN} & \text{otherwise} \end{cases} + 1$$
1 + Piecewise((asinh(sqrt(y^(-2))), (y > -oo)∧(y < oo)∧(Ne(y, 0))), (nan, True))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.