int_(0)^(1)(109)/(1+2^(2))dx=(pi)/(8)log_(2)

int_(0)^(1)(log|1+x|)/(1+x^(2))dx=(pi)/(8)log2

Using property of define integrals, prove that : int_(0)^(1) (log(1+x))/(1+x^(2))=(pi)/8log2

int_(0)^(1)cot^(-1)(1-x+x^(2))dx=(1)(pi)/(2)-log2(2)(pi)/(2)+log2(3)pi-log2(4)pi+log2

int_(0)^( pi/8)(1)/(1+4x^(2))dx=?

If int_(0)^(a)(1)/(1+4x^(2))dx=(pi)/(8) , then a =

int_(0)^(1)((sin^(-1)x)/(x))dx=(pi)/(2)(log2)

If int_(0)^(a) = ( 1)/( 4+x^(2))dx = ( pi)/( 8) then a is

Match the following. {:(I,int_(0)^(pi//2)sqrt(1-cos2x)dx=,(a),2),(II,int_(0)^(pi//2)sqrt(1+sin2x)dx=,(b),sqrt2),(III,int_(0)^(1)(x)/(1+x^(2))dx=,(c),log2),(IV,int_(0)^(pi//2)(cosx)/(1+sinx)dx=,(d),(1)/(2)log2):}

int_(0)^(1)(logx)/(sqrt(1-x^(2)))dx=-(pi)/(2)(log2)

If int_(0)^((pi)/(2))logcosxdx=(pi)/(2)log((1)/(2)) , then int_(0)^((pi)/(2))logsecdx=