`int_(-oo)^(oo)(dx)/(1+x^(2))`

Evaluate : (i) int_(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1)) , (iii) int_(0)^(4)(x^(2))/(1+x)dx (iv) int_(0)^(pi//2) sqrt(costheta)sin^(3)theta

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

int_(0)^(oo)(dx)/((1+x^(2))^(4))=

int_(1)^(oo)(dx)/(x^(2))

I=int_(-oo)^(1)(1)/(x^(2))dx

int_(0)^(oo)(x)/(1+x^(4))dx=

I=int_(0)^(oo)(dx)/(1+e^(x))

Evaluate int _(-oo) ^(oo) (1)/(1 + x ^(2)) dx.

The value of int_(0)^(oo)(dx)/(1+x^(4)) is (a) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x) (b) (pi)/(2sqrt(2))( c) same as that of int_(0)^(oo)(x^(2)+1dx)/(1+x^(4))(d)(pi)/(sqrt(2))