The number of possible solution(s) of the equation `int_0^x(t^2-8t+13)dt = x sin(a/x)` is/are

The number of integral solutions of the equation 4int _(0)^( infty)(In" t"dt)/(x^(2)+t^(2))-piIn 2 =0, x gt 0, is

The number of integral solutions of the equation 4int _(0)^( infty)(In" t"dt)/(x^(2)+t^(2))-piIn 2 =0, x gt 0, is

The solution for x of the equation int_(sqrt2)^(x)(dt)//t(sqrt(t^(2)-1))=(pi)/(2) is

The solution for x of the equation int_(sqrt(2))^(x) (dt)/(|t|sqrt(t^(2)-1))=pi/2 is

Consider the equation int_(theta) ^(x) ( t ^(2) - 8 t + 13) dt = x sin (a / x) The number of real values of x for which the equation has solution is

Number of values of x satisfying the equation int_(-1)^x (8t^2+28/3t+4) \ dt=((3/2)x+1)/(log_(x+1)sqrt(x+1)), is

The total number of distinct x in[0,1] for which int_0^x t^2/(1+t^4) dt =2x-1 is

Number of solution of the equation (d)/(dx)int_(cos x)^( sin x)(dt)/(1-t^(2))=2sqrt(2)in[0,pi] is