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