I=int(sin^(p)x)/(cos^(p+2)x)

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

Find the derivatives w.r.t. x : (sin^(p)x)/(cos^(p+2)x)

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R, then

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

I=int(sin x)/(cos x)dx

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

Find the following integrals: ( i ) int(sin x+cos x)dx( ii) int cos ecx(cos ecx+cos x)dx( iii) int(1-sin x)/(cos^(2)x)dx

Evaluate: (i) int sin^(3)x cos^(5)xdx (ii) int(1)/(sin^(4)x cos^(2)x)dx

Evaluate: (i) int(sin^(2)x)/(1+cos x)dx (ii) int(sec^(2)x+cos ec^(2)x)dx