`int_0^1xsin^(- 1)x dx`

Evaluate the following integral: int_0^(1//2)(xsin^(-1)x)/(sqrt(1-x^2))dx

int_0^1 sin^-1x dx=pi/2-1

int_0^1 sin^-1 x dx=pi/2-1

Evaluate int_(0)^(1//2)(xsin^(-1)x)/(sqrt(1-x^(2)))dx .

(i) int_0^1 x sqrt(2-x) dx (ii) int_0^1 x^2(1-x)^n dx

int_0^1 x/sqrt(1+x)dx

Find: int_0^1x (tan^-1 x)^2 dx

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

int_-a^a(1+x^3)^(-1)dx= (A) 0 (B) 2int_0^a(1-x^6)^(-1)dx (C) 2int_0^a(1+x^3)^(-1)dx (D) 2int_0^a[1+(a-x^3)]^(-1)dx

If int_(0)^(1) tan^(-1) x dx = p , then the value of int_(0)^(1) tan^(-1)((1-x)/(1 +x)) dx is