Sr Examen
Integral de sin^4(1-2x) dx
Solución
Ha introducido
[src]
1 / | | 4 | sin (1 - 2*x) dx | / 0
$$\int\limits_{0}^{1} \sin^{4}{\left(1 - 2 x \right)}\, dx$$
Integral(sin(1 - 2*x)^4, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 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)
$$\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}$$
Gráfica
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
$$- \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8}$$
=
=
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
$$- \frac{5 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{8} - \frac{3 \sin{\left(1 \right)} \cos^{3}{\left(1 \right)}}{8} + \frac{3 \cos^{4}{\left(1 \right)}}{8} + \frac{3 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{4} + \frac{3 \sin^{4}{\left(1 \right)}}{8}$$
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
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.