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