Sr Examen
Integral de sin^2x/cos^5x dx
Solución
Ha introducido
[src]
1 / | | 2 | sin (x) | ------- dx | 5 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx$$
Integral(sin(x)^2/cos(x)^5, (x, 0, 1))
Respuesta (Indefinida)
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/ | | 2 3 | sin (x) log(1 + sin(x)) log(-1 + sin(x)) sin (x) + sin(x) | ------- dx = C - --------------- + ---------------- + -------------------------- | 5 16 16 2 4 | cos (x) 8 - 16*sin (x) + 8*sin (x) | /
$$\int \frac{\sin^{2}{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx = C + \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{16} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{16}$$
Gráfica
Respuesta
[src]
3
log(1 + sin(1)) log(1 - sin(1)) sin (1) + sin(1)
- --------------- + --------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} + \sin{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8}$$
=
=
3
log(1 + sin(1)) log(1 - sin(1)) sin (1) + sin(1)
- --------------- + --------------- + --------------------------
16 16 2 4
8 - 16*sin (1) + 8*sin (1)
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} + \sin{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8}$$
-log(1 + sin(1))/16 + log(1 - sin(1))/16 + (sin(1)^3 + sin(1))/(8 - 16*sin(1)^2 + 8*sin(1)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.