(ii) `int(n+1)/(n^(2)+1)dx`

int(1)/(x(x^(n)+1))dx

int(1)/(x+x^(-n))dx=

int(1)/((x^(2)+k)^(n))dx

Statement-1: int_(0)^(npi+v)|sin x|dx=2n+1-cos v where n in N and 0 le v lt pi . Stetement-2: If f(x) is a periodic function with period T, then (i) int_(0)^(nT) f(x)dx=n int_(0)^(T) f(x)dx , where n in N and (ii) int_(nT)^(nt+a) f(x)dx=int_(0)^(a) f(x) dx , where n in N

Evaluate: int1/(x\ (x^n+1))\ dx (ii) int1/(x(x^5+1))\ dx

int sin^(n)(sin^(-1)x)dx

If I_(n)=int(sin nx)/(sin x)dx, for n>1, then the value of I_(n)-I_(n-2) is

Let C_ (n) = int _ ((1) / (n) +1) ^ ((1) / (n)) (tan ^ (- 1) (nx)) / (sin ^ (- 1) (nx) ) dx then lim_ (n rarr oo) n ^ (2) C_ (n) =

If I_(n)=int(x^(n))/(1+x^(2))dx, where n in N , then : I_(n+2)+I_(n)=

If I_(1)=int_(n)^(e^(2))(dx)/(lnx) and I_(2) = int_(1)^(2)(e^(x))/(x) dx_(1) then