Sr Examen

Otras calculadoras

Resolución de integrales/ sin(x+8)^4

Integral de sin(x+8)^4 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |     4          
 |  sin (x + 8) dx
 |                
/                 
0
∫01sin⁡4(x+8) dx\int\limits_{0}^{1} \sin^{4}{\left(x + 8 \right)}\, dx 
Integral(sin(x + 8)^4, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                      3/    x\                                                               /    x\                                                                                                                                      7/    x\                                                                5/    x\                                                               8/    x\                                                                2/    x\                                                               6/    x\                                                               4/    x\                          
 |                                                 22*tan |4 + -|                                                          6*tan|4 + -|                                                                                                                                 6*tan |4 + -|                                                          22*tan |4 + -|                                                        3*x*tan |4 + -|                                                        12*x*tan |4 + -|                                                       12*x*tan |4 + -|                                                       18*x*tan |4 + -|                          
 |    4                                                   \    2/                                                               \    2/                                                               3*x                                                                     \    2/                                                                 \    2/                                                                \    2/                                                                 \    2/                                                                \    2/                                                                \    2/                          
 | sin (x + 8) dx = C - -------------------------------------------------------------------- - -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + -------------------------------------------------------------------- + --------------------------------------------------------------------
 |                               8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\            8/    x\         2/    x\         6/    x\         4/    x\
/                       8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|   8 + 8*tan |4 + -| + 32*tan |4 + -| + 32*tan |4 + -| + 48*tan |4 + -|
                                  \    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/
∫sin⁡4(x+8) dx=C+3xtan⁡8(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+12xtan⁡6(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+18xtan⁡4(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+12xtan⁡2(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+3x8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+6tan⁡7(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8+22tan⁡5(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8−22tan⁡3(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8−6tan⁡(x2+4)8tan⁡8(x2+4)+32tan⁡6(x2+4)+48tan⁡4(x2+4)+32tan⁡2(x2+4)+8\int \sin^{4}{\left(x + 8 \right)}\, dx = C + \frac{3 x \tan^{8}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{12 x \tan^{6}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{18 x \tan^{4}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{12 x \tan^{2}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{3 x}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{6 \tan^{7}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} + \frac{22 \tan^{5}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} - \frac{22 \tan^{3}{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8} - \frac{6 \tan{\left(\frac{x}{2} + 4 \right)}}{8 \tan^{8}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{6}{\left(\frac{x}{2} + 4 \right)} + 48 \tan^{4}{\left(\frac{x}{2} + 4 \right)} + 32 \tan^{2}{\left(\frac{x}{2} + 4 \right)} + 8}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9001
Trazar el gráfico f(x)
Respuesta [src] 
     4           4           3                  3                  2       2           3                  3          
3*cos (9)   3*sin (9)   5*sin (9)*cos(9)   3*cos (9)*sin(9)   3*cos (9)*sin (9)   3*cos (8)*sin(8)   5*sin (8)*cos(8)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              8                  8                   4                  8                  8
5sin⁡3(8)cos⁡(8)8+3sin⁡(8)cos⁡3(8)8+3sin⁡4(9)8−5sin⁡3(9)cos⁡(9)8+3sin⁡2(9)cos⁡2(9)4−3sin⁡(9)cos⁡3(9)8+3cos⁡4(9)8\frac{5 \sin^{3}{\left(8 \right)} \cos{\left(8 \right)}}{8} + \frac{3 \sin{\left(8 \right)} \cos^{3}{\left(8 \right)}}{8} + \frac{3 \sin^{4}{\left(9 \right)}}{8} - \frac{5 \sin^{3}{\left(9 \right)} \cos{\left(9 \right)}}{8} + \frac{3 \sin^{2}{\left(9 \right)} \cos^{2}{\left(9 \right)}}{4} - \frac{3 \sin{\left(9 \right)} \cos^{3}{\left(9 \right)}}{8} + \frac{3 \cos^{4}{\left(9 \right)}}{8} 
=
= 
     4           4           3                  3                  2       2           3                  3          
3*cos (9)   3*sin (9)   5*sin (9)*cos(9)   3*cos (9)*sin(9)   3*cos (9)*sin (9)   3*cos (8)*sin(8)   5*sin (8)*cos(8)
--------- + --------- - ---------------- - ---------------- + ----------------- + ---------------- + ----------------
    8           8              8                  8                   4                  8                  8
5sin⁡3(8)cos⁡(8)8+3sin⁡(8)cos⁡3(8)8+3sin⁡4(9)8−5sin⁡3(9)cos⁡(9)8+3sin⁡2(9)cos⁡2(9)4−3sin⁡(9)cos⁡3(9)8+3cos⁡4(9)8\frac{5 \sin^{3}{\left(8 \right)} \cos{\left(8 \right)}}{8} + \frac{3 \sin{\left(8 \right)} \cos^{3}{\left(8 \right)}}{8} + \frac{3 \sin^{4}{\left(9 \right)}}{8} - \frac{5 \sin^{3}{\left(9 \right)} \cos{\left(9 \right)}}{8} + \frac{3 \sin^{2}{\left(9 \right)} \cos^{2}{\left(9 \right)}}{4} - \frac{3 \sin{\left(9 \right)} \cos^{3}{\left(9 \right)}}{8} + \frac{3 \cos^{4}{\left(9 \right)}}{8} 
3*cos(9)^4/8 + 3*sin(9)^4/8 - 5*sin(9)^3*cos(9)/8 - 3*cos(9)^3*sin(9)/8 + 3*cos(9)^2*sin(9)^2/4 + 3*cos(8)^3*sin(8)/8 + 5*sin(8)^3*cos(8)/8
Respuesta numérica [src] 
0.442545809567753
0.442545809567753

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

    © Sr Examen – Калькулятор