Sr Examen
Integral de (3*sinx+2*cosx+1)/(sinx+sin(2*x)) dx
Solución
Ha introducido
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1 / | | 3*sin(x) + 2*cos(x) + 1 | ----------------------- dx | sin(x) + sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\left(3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx$$
Integral((3*sin(x) + 2*cos(x) + 1)/(sin(x) + sin(2*x)), (x, 0, 1))
Respuesta (Indefinida)
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/ / / / | | | | | 3*sin(x) + 2*cos(x) + 1 | cos(x) | sin(x) | 1 | ----------------------- dx = C + 2* | ----------------- dx + 3* | ----------------- dx + | ----------------- dx | sin(x) + sin(2*x) | sin(x) + sin(2*x) | sin(x) + sin(2*x) | sin(x) + sin(2*x) | | | | / / / /
$$\int \frac{\left(3 \sin{\left(x \right)} + 2 \cos{\left(x \right)}\right) + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx = C + 3 \int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx + 2 \int \frac{\cos{\left(x \right)}}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx + \int \frac{1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx$$
Respuesta
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1 / | | 1 + 2*cos(x) + 3*sin(x) | ----------------------- dx | sin(x) + sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx$$
=
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1 / | | 1 + 2*cos(x) + 3*sin(x) | ----------------------- dx | sin(x) + sin(2*x) | / 0
$$\int\limits_{0}^{1} \frac{3 \sin{\left(x \right)} + 2 \cos{\left(x \right)} + 1}{\sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx$$
Integral((1 + 2*cos(x) + 3*sin(x))/(sin(x) + sin(2*x)), (x, 0, 1))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.