Sr Examen
Integral de (cos*x*d*x)/(sin^5*x) dx
Solución
Ha introducido
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1 / | | cos(x)*d*x | ---------- dx | 5 | sin (x) | / 0
$$\int\limits_{0}^{1} \frac{x d \cos{\left(x \right)}}{\sin^{5}{\left(x \right)}}\, dx$$
Integral(((cos(x)*d)*x)/sin(x)^5, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ / 3/x\ /x\ 2/x\ 4/x\\ | | tan |-| 3*tan|-| x*tan |-| x*tan |-|| | cos(x)*d*x | 3*x 3 1 \2/ \2/ x \2/ x \2/| | ---------- dx = C + d*|- --- - --------- - ---------- + ------- + -------- - ---------- - --------- - ---------- - ---------| | 5 | 32 /x\ 3/x\ 96 32 2/x\ 16 4/x\ 64 | | sin (x) | 32*tan|-| 96*tan |-| 16*tan |-| 64*tan |-| | | \ \2/ \2/ \2/ \2/ / /
$$\int \frac{x d \cos{\left(x \right)}}{\sin^{5}{\left(x \right)}}\, dx = C + d \left(- \frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{64} - \frac{x \tan^{2}{\left(\frac{x}{2} \right)}}{16} - \frac{3 x}{32} - \frac{x}{16 \tan^{2}{\left(\frac{x}{2} \right)}} - \frac{x}{64 \tan^{4}{\left(\frac{x}{2} \right)}} + \frac{\tan^{3}{\left(\frac{x}{2} \right)}}{96} + \frac{3 \tan{\left(\frac{x}{2} \right)}}{32} - \frac{3}{32 \tan{\left(\frac{x}{2} \right)}} - \frac{1}{96 \tan^{3}{\left(\frac{x}{2} \right)}}\right)$$
Respuesta
[src]
/ 2 4 3 \
| 3 3 1 tan (1/2) 1 tan (1/2) 1 tan (1/2) 3*tan(1/2)|
oo*sign(d) + d*|- -- - ----------- - ------------ - --------- - ------------ - --------- - ------------ + --------- + ----------|
| 32 32*tan(1/2) 2 16 4 64 3 96 32 |
\ 16*tan (1/2) 64*tan (1/2) 96*tan (1/2) /
$$d \left(- \frac{1}{16 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{1}{64 \tan^{4}{\left(\frac{1}{2} \right)}} - \frac{3}{32 \tan{\left(\frac{1}{2} \right)}} - \frac{3}{32} - \frac{1}{96 \tan^{3}{\left(\frac{1}{2} \right)}} - \frac{\tan^{2}{\left(\frac{1}{2} \right)}}{16} - \frac{\tan^{4}{\left(\frac{1}{2} \right)}}{64} + \frac{\tan^{3}{\left(\frac{1}{2} \right)}}{96} + \frac{3 \tan{\left(\frac{1}{2} \right)}}{32}\right) + \infty \operatorname{sign}{\left(d \right)}$$
=
=
/ 2 4 3 \
| 3 3 1 tan (1/2) 1 tan (1/2) 1 tan (1/2) 3*tan(1/2)|
oo*sign(d) + d*|- -- - ----------- - ------------ - --------- - ------------ - --------- - ------------ + --------- + ----------|
| 32 32*tan(1/2) 2 16 4 64 3 96 32 |
\ 16*tan (1/2) 64*tan (1/2) 96*tan (1/2) /
$$d \left(- \frac{1}{16 \tan^{2}{\left(\frac{1}{2} \right)}} - \frac{1}{64 \tan^{4}{\left(\frac{1}{2} \right)}} - \frac{3}{32 \tan{\left(\frac{1}{2} \right)}} - \frac{3}{32} - \frac{1}{96 \tan^{3}{\left(\frac{1}{2} \right)}} - \frac{\tan^{2}{\left(\frac{1}{2} \right)}}{16} - \frac{\tan^{4}{\left(\frac{1}{2} \right)}}{64} + \frac{\tan^{3}{\left(\frac{1}{2} \right)}}{96} + \frac{3 \tan{\left(\frac{1}{2} \right)}}{32}\right) + \infty \operatorname{sign}{\left(d \right)}$$
oo*sign(d) + d*(-3/32 - 3/(32*tan(1/2)) - 1/(16*tan(1/2)^2) - tan(1/2)^2/16 - 1/(64*tan(1/2)^4) - tan(1/2)^4/64 - 1/(96*tan(1/2)^3) + tan(1/2)^3/96 + 3*tan(1/2)/32)
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.