" I."sin^(2)(2x+5)

I=int sin^(2)x*cos^(5)xdx

int((sin2x+sin5x-sin3x)/(cos x+1-2sin^(2)2x))dx

int(sin2x+sin5x-sin3x)/(cos x+1-2sin^(2)2x)dx

I= int sin^(5/2)(x^(3))*cos(x^(3))*x^(2)*dx

Prove that the value of each the following determinants is zero: sin^(2)(x+(3 pi)/(2))quad sin^(2)(x+(5 pi)/(2))quad sin^(2)(x+(7 pi)/(2))sin(x+(3 pi)/(2))quad sin(x+(5 pi)/(2))quad sin(x+(7 pi)/(2))sin(x-(3 pi)/(2))quad sin(x-(5 pi)/(2))quad sin(x-(7 pi)/(2))

Solve (i)7cos^(2)theta+3sin^(2)theta=4(ii)2sin^(2)x+sin^(2)2x=2( iii) 4sin x sin2x sin4x=sin3x

if I=int(x^(2)+20)/((x sin x+5cosx)^(2))dx ,then I equals-

If /_\ = |[5+sin^(2)x,cos^(2)x,4sin2x],[sin^(2)x,5+cos^(2)x,4sin2x],[sin^(2)x,cos^(2)x,5+4sin2x]| =