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Resolución de integrales/ sin^4/ (1-2x)/ sin^4(1-2x)

Integral de sin^4(1-2x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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 |  sin (1 - 2*x) dx
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∫01sin⁡4(1−2x) dx\int\limits_{0}^{1} \sin^{4}{\left(1 - 2 x \right)}\, dx 
Integral(sin(1 - 2*x)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
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 |                                                             3                                                                                                                                                                                                                                                        7                                                                                  5                                                                                   8                                                                                  2                                                                                  6                                                                                  4                                         
 |    4                                                  11*tan (-1/2 + x)                                                                   3*tan(-1/2 + x)                                                                          3*x                                                                          3*tan (-1/2 + x)                                                                  11*tan (-1/2 + x)                                                                  3*x*tan (-1/2 + x)                                                                12*x*tan (-1/2 + x)                                                                12*x*tan (-1/2 + x)                                                                18*x*tan (-1/2 + x)                               
 | sin (1 - 2*x) dx = C - -------------------------------------------------------------------------------- - -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + -------------------------------------------------------------------------------- + --------------------------------------------------------------------------------
 |                                 8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4                      8                   2                   6                   4          
/                         8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)   8 + 8*tan (-1/2 + x) + 32*tan (-1/2 + x) + 32*tan (-1/2 + x) + 48*tan (-1/2 + x)
∫sin⁡4(1−2x) dx=C+3xtan⁡8(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+12xtan⁡6(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+18xtan⁡4(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+12xtan⁡2(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+3x8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+3tan⁡7(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8+11tan⁡5(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8−11tan⁡3(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8−3tan⁡(x−12)8tan⁡8(x−12)+32tan⁡6(x−12)+48tan⁡4(x−12)+32tan⁡2(x−12)+8\int \sin^{4}{\left(1 - 2 x \right)}\, dx = C + \frac{3 x \tan^{8}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{12 x \tan^{6}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{18 x \tan^{4}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{12 x \tan^{2}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{3 x}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{3 \tan^{7}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} + \frac{11 \tan^{5}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} - \frac{11 \tan^{3}{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8} - \frac{3 \tan{\left(x - \frac{1}{2} \right)}}{8 \tan^{8}{\left(x - \frac{1}{2} \right)} + 32 \tan^{6}{\left(x - \frac{1}{2} \right)} + 48 \tan^{4}{\left(x - \frac{1}{2} \right)} + 32 \tan^{2}{\left(x - \frac{1}{2} \right)} + 8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Trazar el gráfico f(x)
Respuesta [src] 
     4           4           3                  3                  2       2   
3*cos (1)   3*sin (1)   5*sin (1)*cos(1)   3*cos (1)*sin(1)   3*cos (1)*sin (1)
--------- + --------- - ---------------- - ---------------- + -----------------
    8           8              8                  8                   4
−5sin⁡3(1)cos⁡(1)8−3sin⁡(1)cos⁡3(1)8+3cos⁡4(1)8+3sin⁡2(1)cos⁡2(1)4+3sin⁡4(1)8- \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8} 
=
= 
     4           4           3                  3                  2       2   
3*cos (1)   3*sin (1)   5*sin (1)*cos(1)   3*cos (1)*sin(1)   3*cos (1)*sin (1)
--------- + --------- - ---------------- - ---------------- + -----------------
    8           8              8                  8                   4
−5sin⁡3(1)cos⁡(1)8−3sin⁡(1)cos⁡3(1)8+3cos⁡4(1)8+3sin⁡2(1)cos⁡2(1)4+3sin⁡4(1)8- \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8} 
3*cos(1)^4/8 + 3*sin(1)^4/8 - 5*sin(1)^3*cos(1)/8 - 3*cos(1)^3*sin(1)/8 + 3*cos(1)^2*sin(1)^2/4
Respuesta numérica [src] 
0.124025565315207
0.124025565315207

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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