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