Sr Examen
Integral de dx/(8-4sinx+7cosx) dx
Solución
Ha introducido
[src]
1 / | | 1 | ----------------------- dx | 8 - 4*sin(x) + 7*cos(x) | / 0
$$\int\limits_{0}^{1} \frac{1}{\left(8 - 4 \sin{\left(x \right)}\right) + 7 \cos{\left(x \right)}}\, dx$$
Integral(1/(8 - 4*sin(x) + 7*cos(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | | 1 / /x\\ / /x\\ | ----------------------- dx = C - log|-3 + tan|-|| + log|-5 + tan|-|| | 8 - 4*sin(x) + 7*cos(x) \ \2// \ \2// | /
$$\int \frac{1}{\left(8 - 4 \sin{\left(x \right)}\right) + 7 \cos{\left(x \right)}}\, dx = C + \log{\left(\tan{\left(\frac{x}{2} \right)} - 5 \right)} - \log{\left(\tan{\left(\frac{x}{2} \right)} - 3 \right)}$$
Gráfica
Respuesta
[src]
-log(5) - log(3 - tan(1/2)) + log(3) + log(5 - tan(1/2))
$$- \log{\left(5 \right)} - \log{\left(3 - \tan{\left(\frac{1}{2} \right)} \right)} + \log{\left(3 \right)} + \log{\left(5 - \tan{\left(\frac{1}{2} \right)} \right)}$$
=
=
-log(5) - log(3 - tan(1/2)) + log(3) + log(5 - tan(1/2))
$$- \log{\left(5 \right)} - \log{\left(3 - \tan{\left(\frac{1}{2} \right)} \right)} + \log{\left(3 \right)} + \log{\left(5 - \tan{\left(\frac{1}{2} \right)} \right)}$$
-log(5) - log(3 - tan(1/2)) + log(3) + log(5 - tan(1/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.