(ii) `int(x^n+n^x+x/n+n/x-n/x^n)dx`

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

int x ^ (2n-1) cos x ^ (n) dx

int x^(3)cos x^(4)dx int nx^(n-1)cos x^(n)dx

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

int(x^(n-1))/(sqrt(1+4x^(n)))dx

if phi (x) = lim_ (x rarr oo) (x ^ (n) -x ^ (- n)) / (x ^ (n) + x ^ (- n)) then int sin ^ (- 1) x phi (x) 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

int(2x^(n-1))/(x^(n)+3)dx