13.-int_(2)^(1)(dx)/(x)=?

Evaluate the following : int_(-2)^(1)(dx)/(x^(2)+4x+13)

int_(2)^(-13)(dx)/(root(5)((3-x)^(4)))

Show that (a) int_(e)^(e^(2))(1)/(log x)dx = int_(1)^(2)(e^(x))/(x)dx (b) int_(t)^(1)(dx)/(1+x^(2)) = int_(1)^(1//t)(dx)/(1+x^(2))

int_(-1)^(1)(x-[2x])dx=

int_(-2)^(2)(dx)/(1+|x-1|)

Show that int_(e)^(e^(2))(1)/(log x) dx = int_(1)^(2)(e^(x))/(x) dx

If int_(0)^(1)f(x)dx=1, int_(0)^(1)x f(x)dx=a and int_(0)^(1)x^(2)f(x)dx=a^(2) , then : int_(0)^(1)(a-x)^(2)f(x)dx=

If int_(0)^(b)(dx)/(1+x^(2))=int_(b)^(oo)(dx)/(1+x_(2)), then b=

If int_(0)^(b)(dx)/(1+x^(2))=int_(b)^( oo)(dx)/(1+x^(2)) , then b=