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Resolución de integrales/ cos^2/ (2x+5)/ cos^2(2x+5)^2

Integral de cos^2(2x+5)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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∫01cos⁡4(2x+5) dx\int\limits_{0}^{1} \cos^{4}{\left(2 x + 5 \right)}\, dx 
Integral(cos(2*x + 5)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
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 |                                                           7                                                                              3                                                                                                                                                             5                                                                                                                                                              8                                                                               2                                                                              6                                                                              4                                      
 |    4                                                 5*tan (5/2 + x)                                                                3*tan (5/2 + x)                                                                      3*x                                                                      3*tan (5/2 + x)                                                                 5*tan(5/2 + x)                                                               3*x*tan (5/2 + x)                                                              12*x*tan (5/2 + x)                                                             12*x*tan (5/2 + x)                                                             18*x*tan (5/2 + x)                             
 | cos (2*x + 5) 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 (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)   8 + 8*tan (5/2 + x) + 32*tan (5/2 + x) + 32*tan (5/2 + x) + 48*tan (5/2 + x)
∫cos⁡4(2x+5) dx=C+3xtan⁡8(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+12xtan⁡6(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+18xtan⁡4(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+12xtan⁡2(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+3x8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8−5tan⁡7(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+3tan⁡5(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8−3tan⁡3(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8+5tan⁡(x+52)8tan⁡8(x+52)+32tan⁡6(x+52)+48tan⁡4(x+52)+32tan⁡2(x+52)+8\int \cos^{4}{\left(2 x + 5 \right)}\, dx = C + \frac{3 x \tan^{8}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{12 x \tan^{6}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{18 x \tan^{4}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{12 x \tan^{2}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{3 x}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} - \frac{5 \tan^{7}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{3 \tan^{5}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} - \frac{3 \tan^{3}{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8} + \frac{5 \tan{\left(x + \frac{5}{2} \right)}}{8 \tan^{8}{\left(x + \frac{5}{2} \right)} + 32 \tan^{6}{\left(x + \frac{5}{2} \right)} + 48 \tan^{4}{\left(x + \frac{5}{2} \right)} + 32 \tan^{2}{\left(x + \frac{5}{2} \right)} + 8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta [src] 
     4           4           3                  3                  2       2           3                  3          
3*cos (7)   3*sin (7)   5*cos (5)*sin(5)   3*sin (5)*cos(5)   3*cos (7)*sin (7)   3*sin (7)*cos(7)   5*cos (7)*sin(7)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              16                 16                  4                  16                 16
−5sin⁡(5)cos⁡3(5)16+3sin⁡3(7)cos⁡(7)16−3sin⁡3(5)cos⁡(5)16+3sin⁡4(7)8+5sin⁡(7)cos⁡3(7)16+3cos⁡4(7)8+3sin⁡2(7)cos⁡2(7)4- \frac{5 \sin{\left(5 \right)} \cos^{3}{\left(5 \right)}}{16} + \frac{3 \sin^{3}{\left(7 \right)} \cos{\left(7 \right)}}{16} - \frac{3 \sin^{3}{\left(5 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin^{4}{\left(7 \right)}}{8} + \frac{5 \sin{\left(7 \right)} \cos^{3}{\left(7 \right)}}{16} + \frac{3 \cos^{4}{\left(7 \right)}}{8} + \frac{3 \sin^{2}{\left(7 \right)} \cos^{2}{\left(7 \right)}}{4} 
=
= 
     4           4           3                  3                  2       2           3                  3          
3*cos (7)   3*sin (7)   5*cos (5)*sin(5)   3*sin (5)*cos(5)   3*cos (7)*sin (7)   3*sin (7)*cos(7)   5*cos (7)*sin(7)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              16                 16                  4                  16                 16
−5sin⁡(5)cos⁡3(5)16+3sin⁡3(7)cos⁡(7)16−3sin⁡3(5)cos⁡(5)16+3sin⁡4(7)8+5sin⁡(7)cos⁡3(7)16+3cos⁡4(7)8+3sin⁡2(7)cos⁡2(7)4- \frac{5 \sin{\left(5 \right)} \cos^{3}{\left(5 \right)}}{16} + \frac{3 \sin^{3}{\left(7 \right)} \cos{\left(7 \right)}}{16} - \frac{3 \sin^{3}{\left(5 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin^{4}{\left(7 \right)}}{8} + \frac{5 \sin{\left(7 \right)} \cos^{3}{\left(7 \right)}}{16} + \frac{3 \cos^{4}{\left(7 \right)}}{8} + \frac{3 \sin^{2}{\left(7 \right)} \cos^{2}{\left(7 \right)}}{4} 
3*cos(7)^4/8 + 3*sin(7)^4/8 - 5*cos(5)^3*sin(5)/16 - 3*sin(5)^3*cos(5)/16 + 3*cos(7)^2*sin(7)^2/4 + 3*sin(7)^3*cos(7)/16 + 5*cos(7)^3*sin(7)/16
Respuesta numérica [src] 
0.556796691722721
0.556796691722721

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

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