Sr Examen
Integral de (sin(x)*x*dx)/(cos^5*x) dx
Solución
Ha introducido
[src]
1 / | | sin(x)*x | -------- dx | 5 | cos (x) | / 0
$$\int\limits_{0}^{1} \frac{x \sin{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx$$
Integral((sin(x)*x)/cos(x)^5, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ 5/x\ /x\ 7/x\ 3/x\ 8/x\ 2/x\ 6/x\ 4/x\ | 10*tan |-| 6*tan|-| 6*tan |-| 10*tan |-| 3*x*tan |-| 12*x*tan |-| 12*x*tan |-| 18*x*tan |-| | sin(x)*x \2/ \2/ 3*x \2/ \2/ \2/ \2/ \2/ \2/ | -------- dx = C - ------------------------------------------------------ - ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ + ------------------------------------------------------ | 5 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ 2/x\ 6/x\ 8/x\ 4/x\ | cos (x) 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*tan |-| 12 - 48*tan |-| - 48*tan |-| + 12*tan |-| + 72*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/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ \2/ /
$$\int \frac{x \sin{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx = C + \frac{3 x \tan^{8}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{12 x \tan^{6}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{18 x \tan^{4}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{12 x \tan^{2}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{3 x}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12} - \frac{6 \tan{\left(\frac{x}{2} \right)}}{12 \tan^{8}{\left(\frac{x}{2} \right)} - 48 \tan^{6}{\left(\frac{x}{2} \right)} + 72 \tan^{4}{\left(\frac{x}{2} \right)} - 48 \tan^{2}{\left(\frac{x}{2} \right)} + 12}$$
Gráfica
Respuesta
[src]
5 8 7 3 2 6 4
3 10*tan (1/2) 6*tan(1/2) 3*tan (1/2) 6*tan (1/2) 10*tan (1/2) 12*tan (1/2) 12*tan (1/2) 18*tan (1/2)
-------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4
12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)
$$- \frac{6 \tan{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3 \tan^{8}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{6}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{18 \tan^{4}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{2}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12}$$
=
=
5 8 7 3 2 6 4
3 10*tan (1/2) 6*tan(1/2) 3*tan (1/2) 6*tan (1/2) 10*tan (1/2) 12*tan (1/2) 12*tan (1/2) 18*tan (1/2)
-------------------------------------------------------------- - -------------------------------------------------------------- - -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + -------------------------------------------------------------- + --------------------------------------------------------------
2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4 2 6 8 4
12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2) 12 - 48*tan (1/2) - 48*tan (1/2) + 12*tan (1/2) + 72*tan (1/2)
$$- \frac{6 \tan{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} - \frac{10 \tan^{5}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3 \tan^{8}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{6 \tan^{7}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{6}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{18 \tan^{4}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{10 \tan^{3}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{3}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12} + \frac{12 \tan^{2}{\left(\frac{1}{2} \right)}}{- 48 \tan^{2}{\left(\frac{1}{2} \right)} - 48 \tan^{6}{\left(\frac{1}{2} \right)} + 12 \tan^{8}{\left(\frac{1}{2} \right)} + 72 \tan^{4}{\left(\frac{1}{2} \right)} + 12}$$
3/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) - 10*tan(1/2)^5/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) - 6*tan(1/2)/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 3*tan(1/2)^8/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 6*tan(1/2)^7/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 10*tan(1/2)^3/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 12*tan(1/2)^2/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 12*tan(1/2)^6/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4) + 18*tan(1/2)^4/(12 - 48*tan(1/2)^2 - 48*tan(1/2)^6 + 12*tan(1/2)^8 + 72*tan(1/2)^4)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.