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