Sr Examen
Integral de (cos2x)^2/(1-2acosx+(a)^2) dx
Solución
Ha introducido
[src]
pi / | | 2 | cos (2*x) | ------------------ dx | 2 | 1 - 2*acos(x) + a | / -pi
$$\int\limits_{- \pi}^{\pi} \frac{\cos^{2}{\left(2 x \right)}}{a^{2} + \left(1 - 2 \operatorname{acos}{\left(x \right)}\right)}\, dx$$
Integral(cos(2*x)^2/(1 - 2*acos(x) + a^2), (x, -pi, pi))
Respuesta (Indefinida)
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/ / | | | 2 | 2 | cos (2*x) | cos (2*x) | ------------------ dx = C + | ------------------ dx | 2 | 2 | 1 - 2*acos(x) + a | 1 + a - 2*acos(x) | | / /
$$\int \frac{\cos^{2}{\left(2 x \right)}}{a^{2} + \left(1 - 2 \operatorname{acos}{\left(x \right)}\right)}\, dx = C + \int \frac{\cos^{2}{\left(2 x \right)}}{a^{2} - 2 \operatorname{acos}{\left(x \right)} + 1}\, dx$$
Respuesta
[src]
pi / | | 2 | cos (2*x) | ------------------ dx | 2 | 1 + a - 2*acos(x) | / -pi
$$\int\limits_{- \pi}^{\pi} \frac{\cos^{2}{\left(2 x \right)}}{a^{2} - 2 \operatorname{acos}{\left(x \right)} + 1}\, dx$$
=
=
pi / | | 2 | cos (2*x) | ------------------ dx | 2 | 1 + a - 2*acos(x) | / -pi
$$\int\limits_{- \pi}^{\pi} \frac{\cos^{2}{\left(2 x \right)}}{a^{2} - 2 \operatorname{acos}{\left(x \right)} + 1}\, dx$$
Integral(cos(2*x)^2/(1 + a^2 - 2*acos(x)), (x, -pi, pi))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.