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