Sr Examen
Integral de x/cos(x/3)^2 dx
Solución
Ha introducido
[src]
1 / | | x | ------- dx | 2/x\ | cos |-| | \3/ | / 0
$$\int\limits_{0}^{1} \frac{x}{\cos^{2}{\left(\frac{x}{3} \right)}}\, dx$$
Integral(x/cos(x/3)^2, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / /x\\ / /x\\ / 2/x\\ 2/x\ / 2/x\\ /x\ 2/x\ / /x\\ 2/x\ / /x\\ | 9*log|1 + tan|-|| 9*log|-1 + tan|-|| 9*log|1 + tan |-|| 9*tan |-|*log|1 + tan |-|| 6*x*tan|-| 9*tan |-|*log|1 + tan|-|| 9*tan |-|*log|-1 + tan|-|| | x \ \6// \ \6// \ \6// \6/ \ \6// \6/ \6/ \ \6// \6/ \ \6// | ------- dx = C - ----------------- - ------------------ + ------------------ - -------------------------- - ------------ + ------------------------- + -------------------------- | 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ 2/x\ | cos |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| -1 + tan |-| | \3/ \6/ \6/ \6/ \6/ \6/ \6/ \6/ | /
$$\int \frac{x}{\cos^{2}{\left(\frac{x}{3} \right)}}\, dx = C - \frac{6 x \tan{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} + \frac{9 \log{\left(\tan{\left(\frac{x}{6} \right)} - 1 \right)} \tan^{2}{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} - \frac{9 \log{\left(\tan{\left(\frac{x}{6} \right)} - 1 \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} + \frac{9 \log{\left(\tan{\left(\frac{x}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} - \frac{9 \log{\left(\tan{\left(\frac{x}{6} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} - \frac{9 \log{\left(\tan^{2}{\left(\frac{x}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{x}{6} \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1} + \frac{9 \log{\left(\tan^{2}{\left(\frac{x}{6} \right)} + 1 \right)}}{\tan^{2}{\left(\frac{x}{6} \right)} - 1}$$
Gráfica
Respuesta
[src]
/ 2 \ 2 / 2 \ 2 2
9*(pi*I + log(1 - tan(1/6))) 9*log(1 + tan(1/6)) 6*tan(1/6) 9*log\1 + tan (1/6)/ 9*tan (1/6)*log\1 + tan (1/6)/ 9*tan (1/6)*(pi*I + log(1 - tan(1/6))) 9*tan (1/6)*log(1 + tan(1/6))
-9*pi*I - ---------------------------- - ------------------- - -------------- + -------------------- - ------------------------------ + -------------------------------------- + -----------------------------
2 2 2 2 2 2 2
-1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6)
$$\frac{9 \log{\left(\tan^{2}{\left(\frac{1}{6} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} + \frac{9 \log{\left(\tan{\left(\frac{1}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \log{\left(\tan^{2}{\left(\frac{1}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{6 \tan{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \log{\left(\tan{\left(\frac{1}{6} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - 9 i \pi + \frac{9 \left(\log{\left(1 - \tan{\left(\frac{1}{6} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \left(\log{\left(1 - \tan{\left(\frac{1}{6} \right)} \right)} + i \pi\right)}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}}$$
=
=
/ 2 \ 2 / 2 \ 2 2
9*(pi*I + log(1 - tan(1/6))) 9*log(1 + tan(1/6)) 6*tan(1/6) 9*log\1 + tan (1/6)/ 9*tan (1/6)*log\1 + tan (1/6)/ 9*tan (1/6)*(pi*I + log(1 - tan(1/6))) 9*tan (1/6)*log(1 + tan(1/6))
-9*pi*I - ---------------------------- - ------------------- - -------------- + -------------------- - ------------------------------ + -------------------------------------- + -----------------------------
2 2 2 2 2 2 2
-1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6) -1 + tan (1/6)
$$\frac{9 \log{\left(\tan^{2}{\left(\frac{1}{6} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} + \frac{9 \log{\left(\tan{\left(\frac{1}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \log{\left(\tan^{2}{\left(\frac{1}{6} \right)} + 1 \right)} \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{6 \tan{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \log{\left(\tan{\left(\frac{1}{6} \right)} + 1 \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - 9 i \pi + \frac{9 \left(\log{\left(1 - \tan{\left(\frac{1}{6} \right)} \right)} + i \pi\right) \tan^{2}{\left(\frac{1}{6} \right)}}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}} - \frac{9 \left(\log{\left(1 - \tan{\left(\frac{1}{6} \right)} \right)} + i \pi\right)}{-1 + \tan^{2}{\left(\frac{1}{6} \right)}}$$
-9*pi*i - 9*(pi*i + log(1 - tan(1/6)))/(-1 + tan(1/6)^2) - 9*log(1 + tan(1/6))/(-1 + tan(1/6)^2) - 6*tan(1/6)/(-1 + tan(1/6)^2) + 9*log(1 + tan(1/6)^2)/(-1 + tan(1/6)^2) - 9*tan(1/6)^2*log(1 + tan(1/6)^2)/(-1 + tan(1/6)^2) + 9*tan(1/6)^2*(pi*i + log(1 - tan(1/6)))/(-1 + tan(1/6)^2) + 9*tan(1/6)^2*log(1 + tan(1/6))/(-1 + tan(1/6)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.