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

For integral int f(x- a/x)*(1+a/x^(2))dx , put x-a/x=t For integral int f(x+a/x)*(1-(a)/(x^(2)))dx , put x+a/x =t For integral int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx , put x^(2)-(a)/(x^(2))=t For integral int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx , put x^(2)+(a)/(x^(2))=t many integrands can be brought into above forms by suitable reductions or transformations . int((x-1))/((x+1)sqrt(x^(3)+x^(2)+x))dx

For integral int f(x- a/x)*(1+a/x^(2))dx , put x-a/x=t For integral int f(x+a/x)*(1-(a)/(x^(2)))dx , put x+a/x =t For integral int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx , put x^(2)-(a)/(x^(2))=t For integral int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx , put x^(2)+(a)/(x^(2))=t many integrands can be brought into above forms by suitable reductions or transformations . int(x^(4)-2)/(x^(2)sqrt(x^(4)+x^(2)+2))dx

For integral int f(x- a/x)*(1+a/x^(2))dx , put x-a/x=t For integral int f(x+a/x)*(1-(a)/(x^(2)))dx , put x+a/x =t For integral int f(x^(2)-(a)/(x^(2)))*(x+(a)/(x^(3)))dx , put x^(2)-(a)/(x^(2))=t For integral int f(x^(2)+(a)/(x^(2)))*(x-(a)/(x^(3)))dx , put x^(2)+(a)/(x^(2))=t many integrands can be brought into above forms by suitable reductions or transformations . int(5x^(4)+4x^(5))/((x^(5)+x+1)^(2))dx

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

int(dx)/(xsqrt(x^(2n)-a^(2n)))

Evaluate: inte^x(1+n x^(n-1)-x^(2n))/((1-x^n)sqrt(1-x^(2n)))dx

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

Evaluate the following integral int(x^(2)+2x+3)/(sqrt(x^(2)+x+1))dx

Evaluate the following integration int(x^(2)+3)/(x^(6)(x^(2)+1))dx

Evaluate of each of the following integral: int_a^b(x^(1//n))/(x^(1//n)+(a+b-x)^(1/n))dx , \ ngeq2