`I=int_(0)^(1)tan^(-1)xdx`

Let J=int_(0)^(1)cot^(-1)(1-x+x^(2))dx and K= int_(0)^(1)tan^(-1)xdx .If J=lambda K (lambda in N) , then lambda equals

If int_(0)^(1) cot^(-1)(1-x+x^(2))dx=k int_(0)^(1) tan^(-1)x dx , then k=

STATEMENT-1 : int_(-3)^(3)|x|dx=9 STATEMENT-2 : int_(0)^(1)tan^(-1)xdx=(pi)/(4)-lnsqrt(2) STATEMENT-3 : int_(0)^(pi//2)(sqrt(cosx))/(sqrt(sinx)+sqrt(cosx))dx=(pi)/(4)

int_(0)^( pi)x sin^(-1)xdx

I=int_(0)^( pi/4)(tan^(-1)x)^(2)/(1+x^2)dx

Evaluate : (i) int_(0)^(1)sin^(-1)xdx , (ii) int_(1)^(2)(lnx)/(x^(2))dx , (iii) int_(0)^(1)x^(2)sin^(-1)xdx .

Let I_(n) = int_(0)^(1)x^(n)(tan^(1)x)dx, n in N , then

Evaluate : (i) int_(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) int_(0)^(1)x cos(tan^(1)x)dx

The value of int_(0)^(1)(tan^(-1)((x)/(x+1)))/(tan^(-1)((1+2x-2x^(2))/(2)))dx is

The value of int_(0)^(1) tan^(-1)((2x-1)/(1+x-x^(2)))dx is