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

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

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

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

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

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

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

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

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