Sr Examen
Integral de ((1-sin(x))^2)/(1+sinx) dx
Solución
Ha introducido
[src]
1 / | | 2 | (1 - sin(x)) | ------------- dx | 1 + sin(x) | / 0
$$\int\limits_{0}^{1} \frac{\left(1 - \sin{\left(x \right)}\right)^{2}}{\sin{\left(x \right)} + 1}\, dx$$
Integral((1 - sin(x))^2/(1 + sin(x)), (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 2/x\ /x\ 2/x\ 3/x\ /x\ /x\ | 2 2*tan |-| 2*tan|-| x*tan |-| x*tan |-| x*tan|-| 2*x*tan|-| | (1 - sin(x)) 6 4 x 2*x \2/ \2/ \2/ \2/ \2/ \2/ | ------------- dx = C - ---------- - ------------------------------ - ------------------------------ - ---------- - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------ - ------------------------------ - ---------- | 1 + sin(x) /x\ 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ /x\ 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ 2/x\ 3/x\ /x\ /x\ | 1 + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan |-| + tan |-| + tan|-| 1 + tan|-| / \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/
$$\int \frac{\left(1 - \sin{\left(x \right)}\right)^{2}}{\sin{\left(x \right)} + 1}\, dx = C - \frac{x \tan^{3}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x \tan{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{x}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 x \tan{\left(\frac{x}{2} \right)}}{\tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 x}{\tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{4}{\tan^{3}{\left(\frac{x}{2} \right)} + \tan^{2}{\left(\frac{x}{2} \right)} + \tan{\left(\frac{x}{2} \right)} + 1} - \frac{6}{\tan{\left(\frac{x}{2} \right)} + 1}$$
Gráfica
Respuesta
[src]
2 3
13 11*tan (1/2) 5*tan(1/2) 3*tan (1/2)
10 - ------------------------------------ - ------------------------------------ - ------------------------------------ - ------------------------------------
2 3 2 3 2 3 2 3
1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2)
$$- \frac{13}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{11 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{5 \tan{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan^{3}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} + 10$$
=
=
2 3
13 11*tan (1/2) 5*tan(1/2) 3*tan (1/2)
10 - ------------------------------------ - ------------------------------------ - ------------------------------------ - ------------------------------------
2 3 2 3 2 3 2 3
1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2) 1 + tan (1/2) + tan (1/2) + tan(1/2)
$$- \frac{13}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{11 \tan^{2}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{5 \tan{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} - \frac{3 \tan^{3}{\left(\frac{1}{2} \right)}}{\tan^{3}{\left(\frac{1}{2} \right)} + \tan^{2}{\left(\frac{1}{2} \right)} + \tan{\left(\frac{1}{2} \right)} + 1} + 10$$
10 - 13/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - 11*tan(1/2)^2/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - 5*tan(1/2)/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2)) - 3*tan(1/2)^3/(1 + tan(1/2)^2 + tan(1/2)^3 + tan(1/2))
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.