Sr Examen
Integral de (sinx+sin³x)dx/cos2x dx
Solución
Ha introducido
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1 / | | 3 | sin(x) + sin (x) | ---------------- dx | cos(2*x) | / 0
$$\int\limits_{0}^{1} \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
Integral((sin(x) + sin(x)^3)/cos(2*x), (x, 0, 1))
Respuesta (Indefinida)
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/ ___ / ___ \
|-\/ 2 *acoth\\/ 2 *cos(x)/ 2
|--------------------------- for cos (x) > 1/2
| 2
<
/ | ___ / ___ \
| |-\/ 2 *atanh\\/ 2 *cos(x)/ 2 /
| 3 |--------------------------- for cos (x) < 1/2 |
| sin(x) + sin (x) \ 2 cos(x) | sin(x)
| ---------------- dx = C + ----------------------------------------------- + ------ + 2* | -------- dx
| cos(2*x) 2 2 | cos(2*x)
| |
/ /
$$\int \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx = C + \frac{\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \cos{\left(x \right)} \right)}}{2} & \text{for}\: \cos^{2}{\left(x \right)} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\sqrt{2} \cos{\left(x \right)} \right)}}{2} & \text{for}\: \cos^{2}{\left(x \right)} < \frac{1}{2} \end{cases}}{2} + \frac{\cos{\left(x \right)}}{2} + 2 \int \frac{\sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.