Sr Examen
Integral de xdx/(sin²x) dx
Solución
Ha introducido
[src]
pi -- 3 / | | x | ------- dx | 2 | sin (x) | / pi -- 44
$$\int\limits_{\frac{\pi}{44}}^{\frac{\pi}{3}} \frac{x}{\sin^{2}{\left(x \right)}}\, dx$$
Integral(x/sin(x)^2, (x, pi/44, pi/3))
Respuesta (Indefinida)
[src]
/ /x\ | x*tan|-| | x / 2/x\\ \2/ x / /x\\ | ------- dx = C - log|1 + tan |-|| + -------- - -------- + log|tan|-|| | 2 \ \2// 2 /x\ \ \2// | sin (x) 2*tan|-| | \2/ /
$$\int \frac{x}{\sin^{2}{\left(x \right)}}\, dx = C + \frac{x \tan{\left(\frac{x}{2} \right)}}{2} - \frac{x}{2 \tan{\left(\frac{x}{2} \right)}} - \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} + \log{\left(\tan{\left(\frac{x}{2} \right)} \right)}$$
Gráfica
Respuesta
[src]
/pi\
___ pi*tan|--| / ___\
/ /pi\\ pi*\/ 3 \88/ pi |\/ 3 | / 2/pi\\
-log(4/3) - log|tan|--|| - -------- - ---------- + ---------- + log|-----| + log|1 + tan |--||
\ \88// 9 88 /pi\ \ 3 / \ \88//
88*tan|--|
\88/
$$- \frac{\sqrt{3} \pi}{9} + \log{\left(\frac{\sqrt{3}}{3} \right)} - \log{\left(\frac{4}{3} \right)} - \frac{\pi \tan{\left(\frac{\pi}{88} \right)}}{88} + \log{\left(\tan^{2}{\left(\frac{\pi}{88} \right)} + 1 \right)} + \frac{\pi}{88 \tan{\left(\frac{\pi}{88} \right)}} - \log{\left(\tan{\left(\frac{\pi}{88} \right)} \right)}$$
=
=
/pi\
___ pi*tan|--| / ___\
/ /pi\\ pi*\/ 3 \88/ pi |\/ 3 | / 2/pi\\
-log(4/3) - log|tan|--|| - -------- - ---------- + ---------- + log|-----| + log|1 + tan |--||
\ \88// 9 88 /pi\ \ 3 / \ \88//
88*tan|--|
\88/
$$- \frac{\sqrt{3} \pi}{9} + \log{\left(\frac{\sqrt{3}}{3} \right)} - \log{\left(\frac{4}{3} \right)} - \frac{\pi \tan{\left(\frac{\pi}{88} \right)}}{88} + \log{\left(\tan^{2}{\left(\frac{\pi}{88} \right)} + 1 \right)} + \frac{\pi}{88 \tan{\left(\frac{\pi}{88} \right)}} - \log{\left(\tan{\left(\frac{\pi}{88} \right)} \right)}$$
-log(4/3) - log(tan(pi/88)) - pi*sqrt(3)/9 - pi*tan(pi/88)/88 + pi/(88*tan(pi/88)) + log(sqrt(3)/3) + log(1 + tan(pi/88)^2)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.