The value of `int_(0)^(pi)(Sigma_(r=0)^(3)a_(r)cos^(3-r)x sin^(r)x)dx` depends upon

The value of int_(0)^(1)(pi_(r=1)^(n)(x+r))(sum_(k=1)^(n)(1)/(x+k))dx

[ The value of int_(-pi)^( pi)sum_(r=0)^(999)cos rx(1+sum_(r=1)^(999)sin rx)dx, is [ (1) 2 pi, (2) 999 pi, (3) 0]]

[ The value of int_(-pi)^( pi)sum_(r=0)^(999)cos rx(1+sum_(r=1)^(999)sin rx) dx, is [ (1) 2 pi, (2) 999 pi, (3) 0]]

The value of int_(-pi)^( pi)sum_(r=0)^(999)cos rx(1+sum_(r=1)^(999)sin rx) dx, is

int_(0)^(oo)(dx)/((x+r)^(3/2))

The value of (sum_(r=0)^(n)nC_(r)sin2 pi x)/(sum_(r=0)^(n)nC_(r)cos2 pi x) is equal to

The value of sum_(r=0)^(10)cos^(3)((r pi)/(3)) is

int(sum_(r)=0^(oo)(x^(r)3^(r))/(r!))dx