Sr Examen
Integral de sinx/(sqr(16+9cosx^2)) dx
Solución
Ha introducido
[src]
pi -- 2 / | | sin(x) | ----------------- dx | 2 | / 2 \ | \16 + 9*cos (x)/ | / 0
$$\int\limits_{0}^{\frac{\pi}{2}} \frac{\sin{\left(x \right)}}{\left(9 \cos^{2}{\left(x \right)} + 16\right)^{2}}\, dx$$
Integral(sin(x)/(16 + 9*cos(x)^2)^2, (x, 0, pi/2))
Respuesta (Indefinida)
[src]
/ /3*cos(x)\ 2 /3*cos(x)\ | 16*atan|--------| 9*cos (x)*atan|--------| | sin(x) \ 4 / 12*cos(x) \ 4 / | ----------------- dx = C - ------------------- - ------------------- - ------------------------ | 2 2 2 2 | / 2 \ 6144 + 3456*cos (x) 6144 + 3456*cos (x) 6144 + 3456*cos (x) | \16 + 9*cos (x)/ | /
$$\int \frac{\sin{\left(x \right)}}{\left(9 \cos^{2}{\left(x \right)} + 16\right)^{2}}\, dx = C - \frac{9 \cos^{2}{\left(x \right)} \operatorname{atan}{\left(\frac{3 \cos{\left(x \right)}}{4} \right)}}{3456 \cos^{2}{\left(x \right)} + 6144} - \frac{12 \cos{\left(x \right)}}{3456 \cos^{2}{\left(x \right)} + 6144} - \frac{16 \operatorname{atan}{\left(\frac{3 \cos{\left(x \right)}}{4} \right)}}{3456 \cos^{2}{\left(x \right)} + 6144}$$
Gráfica
Respuesta
[src]
1 atan(3/4) --- + --------- 800 384
$$\frac{1}{800} + \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{384}$$
=
=
1 atan(3/4) --- + --------- 800 384
$$\frac{1}{800} + \frac{\operatorname{atan}{\left(\frac{3}{4} \right)}}{384}$$
1/800 + atan(3/4)/384
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.