Prove that `int _(-2)^2|1-x^2|dx=4`

Prove that: int_(-2)^(2)|1-x^(2)|dx=4

Prove that int_-2^2 f(x^4)dx=2int_0^2 f(x^4)dx

Prove that int_-2^2 f(x^4)dx=2int_0^2 f(x^4)dx

Prove that : int 1/(a^(2)-x^(2)) dx = 1/(2a) log |(a+x)/(a-x)|+c.

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

Prove that, int (e^(x))/(x^(4))dx=-(e^(x))/(3)[(1)/(x^(3))+(1)/(2x^(2))+(1)/(2x)]+(1)/(6)int (e^(x))/(x)dx .

Prove that int_(0)^1 ((tan^(-1)x)/x) dx=1/2int_(0)^((pi)/2)x/(sinx)dx .

Prove that int_(0)^(tan^(-1)x)/x dx=1/2int_(0)^((pi)/2)x/(sinx)dx .

Prove that int_(0)^(tan^(-1)x)/x dx=1/2int_(0)^((pi)/2)x/(sinx)dx .