Sr Examen
Integral de cos^2(2x+5)^2 dx
Solución
Ha introducido
[src]
1 / | | 4 | cos (2*x + 5) dx | / 0
$$\int\limits_{0}^{1} \cos^{4}{\left(2 x + 5 \right)}\, dx$$
Integral(cos(2*x + 5)^4, (x, 0, 1))
Respuesta (Indefinida)
[src]
/ | 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)
$$\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}$$
Gráfica
Respuesta
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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
$$- \frac{5 \sin{\left(5 \right)} \cos^{3}{\left(5 \right)}}{16} + \frac{3 \sin^{3}{\left(7 \right)} \cos{\left(7 \right)}}{16} - \frac{3 \sin^{3}{\left(5 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin^{4}{\left(7 \right)}}{8} + \frac{5 \sin{\left(7 \right)} \cos^{3}{\left(7 \right)}}{16} + \frac{3 \cos^{4}{\left(7 \right)}}{8} + \frac{3 \sin^{2}{\left(7 \right)} \cos^{2}{\left(7 \right)}}{4}$$
=
=
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
$$- \frac{5 \sin{\left(5 \right)} \cos^{3}{\left(5 \right)}}{16} + \frac{3 \sin^{3}{\left(7 \right)} \cos{\left(7 \right)}}{16} - \frac{3 \sin^{3}{\left(5 \right)} \cos{\left(5 \right)}}{16} + \frac{3 \sin^{4}{\left(7 \right)}}{8} + \frac{5 \sin{\left(7 \right)} \cos^{3}{\left(7 \right)}}{16} + \frac{3 \cos^{4}{\left(7 \right)}}{8} + \frac{3 \sin^{2}{\left(7 \right)} \cos^{2}{\left(7 \right)}}{4}$$
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
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.