If `int (dx)/(3sqrt(cos^(12)x+3cos^(10)x+3cos^8x+cos^6x))=f(x)-1/(sqrt(2))tan^(- 1)(f(x)/(sqrt(2)))+C` ,then `f(x)` is -

int(1)/(sqrt(cos^(3)x cos(x+a)))dx

If int (sinx)/(sin^(2)x+4cos^(2)x)dx=-(1)/(sqrt(3))tan^(-1)((sqrt(3))/f(x))+c ,then f(x) equals :

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))

If int cos^(-1)x+cos^(-1)sqrt(1-x^2) dx= Ax+f(x)sin^(-1)x-2sqrt(1-x^2)+c then

int(sinx)/(3+4cos^2x)\ dx a. log(3+4cos^2x)+C (b) 1/(2sqrt(3))tan^(-1)((cosx)/(sqrt(3)))+C (c) -1/(2sqrt(3))tan^(-1)((2"\ cos"x)/(sqrt(3)))+C (d) 1/(2sqrt(3))tan^(-1)((2"\ cos"x)/(sqrt(3)))+C