int tan sqrt(pi)cos x:int(3x^(2))/(x^(6)+1)dx

For x in(0, (pi)/(2)) If int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then [f((pi)/(4))] = ( where [.] denotes G.I.F )

For x in [0, (pi)/(2)] if int(tan x sqrt(sec x)(1+cos^(2)x))/(sqrt(cos x+sin^(2)x))dx=2sqrt(f(x)+1)+c and f((pi)/(3))=(3)/(2) then f((pi)/(4)) = (where[.] denotes I F)

Evaluate : int tan^(-1){sqrt((1-cos2x)/(1+cos2x))}dx .

If int_(0)^(pi//2) sin^(6) x dx = (pi)/(32) then int_(-pi)^(pi) (sin^(6)x + cos^(6) x)dx=

int_(0)^(pi) sqrt((1+cos 2x)/(2))dx=

int tan^(-1) sqrt((1 - cos 2x)/( 1 + cos 2 x )) dx is

int tan^(-1) sqrt((1 - cos 2 x)/(1 + cos 2x)) dx . ……………. .

int cos6x sqrt(1+sin6x)dx

int tan^(-1)( sqrt((1-cos2x)/(1+cos2x)))dx