Sr Examen
Integral de sin^2(0.25×x)/cos(0.25×x) dx
Solución
Ha introducido
[src]
5 / | | 2/x\ | sin |-| | \4/ | ------- dx | /x\ | cos|-| | \4/ | / 4
$$\int\limits_{4}^{5} \frac{\sin^{2}{\left(\frac{x}{4} \right)}}{\cos{\left(\frac{x}{4} \right)}}\, dx$$
Integral(sin(x/4)^2/cos(x/4), (x, 4, 5))
Respuesta (Indefinida)
[src]
/ | | 2/x\ | sin |-| | \4/ /x\ / /x\\ / /x\\ | ------- dx = C - 4*sin|-| - 2*log|-1 + sin|-|| + 2*log|1 + sin|-|| | /x\ \4/ \ \4// \ \4// | cos|-| | \4/ | /
$$\int \frac{\sin^{2}{\left(\frac{x}{4} \right)}}{\cos{\left(\frac{x}{4} \right)}}\, dx = C - 2 \log{\left(\sin{\left(\frac{x}{4} \right)} - 1 \right)} + 2 \log{\left(\sin{\left(\frac{x}{4} \right)} + 1 \right)} - 4 \sin{\left(\frac{x}{4} \right)}$$
Gráfica
Respuesta
[src]
-4*sin(5/4) - 2*log(1 - sin(5/4)) - 2*log(1 + sin(1)) + 2*log(1 - sin(1)) + 2*log(1 + sin(5/4)) + 4*sin(1)
$$- 4 \sin{\left(\frac{5}{4} \right)} + 2 \log{\left(1 - \sin{\left(1 \right)} \right)} - 2 \log{\left(\sin{\left(1 \right)} + 1 \right)} + 2 \log{\left(\sin{\left(\frac{5}{4} \right)} + 1 \right)} + 4 \sin{\left(1 \right)} - 2 \log{\left(1 - \sin{\left(\frac{5}{4} \right)} \right)}$$
=
=
-4*sin(5/4) - 2*log(1 - sin(5/4)) - 2*log(1 + sin(1)) + 2*log(1 - sin(1)) + 2*log(1 + sin(5/4)) + 4*sin(1)
$$- 4 \sin{\left(\frac{5}{4} \right)} + 2 \log{\left(1 - \sin{\left(1 \right)} \right)} - 2 \log{\left(\sin{\left(1 \right)} + 1 \right)} + 2 \log{\left(\sin{\left(\frac{5}{4} \right)} + 1 \right)} + 4 \sin{\left(1 \right)} - 2 \log{\left(1 - \sin{\left(\frac{5}{4} \right)} \right)}$$
-4*sin(5/4) - 2*log(1 - sin(5/4)) - 2*log(1 + sin(1)) + 2*log(1 - sin(1)) + 2*log(1 + sin(5/4)) + 4*sin(1)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.