" 4."(1)/(sin x*cos x+2cos^(2)x)

int(1)/(4sin^(2)x+3sin x cos x+2 cos^(2)x)dx=

int ((4-5sin x) / (cos ^ (2) x) + (1) / (sin ^ (2) x cos ^ (2) x)) dx

int(1)/(4sin^(2)x+4sin x cos x+5cos^(2)x)dx

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x , then the constant term is

If the determinant |(cos2x,sin^2 x,cos 4x),(sin^2 x,cos 2x,cos^2 x),(cos 4x,cos^2 x,cos 2x)| is expanded in powers of sin x, then the constant term is

When the determinant |{:(cos2x,sin^(2)x,cos4x),(sin^(2)x,cos2x,cos^(2)x),(cos4x,cos^(2)x,cos2x):}| is expanded in powers of sin x , the constant term in than or equal to expression is

When the determinant |{:(cos2x,sin^(2)x,cos4x),(sin^(2)x,cos2x,cos^(2)x),(cos4x,cos^(2)x,cos2x):}| is expanded in powers of sin x , the constant term is equal to expression is

When the determinant |{:(cos2x,,sin^(2)x,,cos4x),(sin^(2)x,,cos2x,,cos^(2)x),(cos4x,,cos^(2)x,,cos 2x):}| expanded in powers of sin x, then the constant term in that expression is