Sr Examen
Integral de (cosx)\(16+sinx^2) dx
Solución
Ha introducido
[src]
5*p --- 6 / | | cos(x) | ------------ dx | 2 | 16 + sin (x) | / p - 2
$$\int\limits_{\frac{p}{2}}^{\frac{5 p}{6}} \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 16}\, dx$$
Integral(cos(x)/(16 + sin(x)^2), (x, p/2, 5*p/6))
Respuesta (Indefinida)
[src]
/ /sin(x)\ | atan|------| | cos(x) \ 4 / | ------------ dx = C + ------------ | 2 4 | 16 + sin (x) | /
$$\int \frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 16}\, dx = C + \frac{\operatorname{atan}{\left(\frac{\sin{\left(x \right)}}{4} \right)}}{4}$$
Respuesta
[src]
/ /p\\ / /5*p\\
|sin|-|| |sin|---||
| \2/| | \ 6 /|
atan|------| atan|--------|
\ 4 / \ 4 /
- ------------ + --------------
4 4
$$- \frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{p}{2} \right)}}{4} \right)}}{4} + \frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{5 p}{6} \right)}}{4} \right)}}{4}$$
=
=
/ /p\\ / /5*p\\
|sin|-|| |sin|---||
| \2/| | \ 6 /|
atan|------| atan|--------|
\ 4 / \ 4 /
- ------------ + --------------
4 4
$$- \frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{p}{2} \right)}}{4} \right)}}{4} + \frac{\operatorname{atan}{\left(\frac{\sin{\left(\frac{5 p}{6} \right)}}{4} \right)}}{4}$$
-atan(sin(p/2)/4)/4 + atan(sin(5*p/6)/4)/4
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.