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