Ayuda?

A) integral de sen ^ 2(x) dx = integral de (2sen ^ 2(x) / 2)dx

integral de ((1 - cos 2x) / 2)dx = integral de( 1 / 2 - cos2x / 2)dx = x / 2 - 1 / 2 integral de cos2xdx + c

x / 2 - 1 / 2 (sen2x / 2) + c

x / 2 - sen2x / 4 + c

b) integral de cos ^ 2(3x)dx = integral de ((2cos ^ 2(3x)) / 2 dx

integral de ((1 + cos6x) / 2)dx = integral de (1 / 2 + cos6x / 2)

x / 2 + integral de cos6x / 2 + c = x / 2 + 1 / 2 (integral de cos6x) = x / 2 + 1 / 2 ( - sen6x / 6) + c = x / 2 - sen6x / 12 + c

c) integral de sen ^ 3 (x)dx = integral de sen ^ 2(x) senxdx = integral de (1 - cos ^ 2(x))senxdx = integral de [(senx) - cos ^ 2(x)senx]dx = integral de senxdx - integral de cos ^ 2(x)senxdx - cosx - ( - cos ^ 3(x) / 3) + c - cosx + (cos ^ 3(x)) / 3 + c

d) integral de sec ^ 4 (2x)dx = integral de sec ^ 2(x) sec ^ 2(x) = integral de (1 + tg ^ 2(x)) sec ^ 2(x) dx = integral de [sec ^ 2(x) + tg ^ 2(x) sec ^ 2(x)] dx = integral de sec ^ 2(x)dx + integral de tg ^ 2(x) sec ^ 2(x) dx = tg(x) + integral de tg ^ 2(x) sec ^ 2(x) dx + c

Sea u = tg(x) = = = = = = 》du = sec ^ 2(x)dx

Entonces = tg(x) + integral de (u ^ 2) du + c = tg(x) + (u ^ 3) / 3 + c = tg(x) + (tg ^ 3(x)) / 3 + c.