int e^(x)[(x^(3)+x+1)/((1+x^(2))^((3)/(2)))]dx=

int e^(x)((x^(2)-3)/((x+3)^(2)))dx

int e^(x)((1)/(x^(2))-(2)/(x^(3)))dx

int(e^(x)(x-3))/((x-1)^(3))dx

(3) int(dx)/(1+e^(2x))

int_(-a)^(a)x^(2)(e^(x^(3))-e^(-x^(3)))/(e^(x^(3))+e^(-x^(3)))dx=

int_(1)^(e) e^(x)((x-1)/(x^(2)))dx=

int(e^(x))/(x^(4))dx=-(e^(x))/(3)[(1)/(x^(3))+(1)/(2x^(2))+(1)/(2x)]+(1)/(6)int(e^(x))/(x)dx

Prove that, int (e^(x))/(x^(4))dx=-(e^(x))/(3)[(1)/(x^(3))+(1)/(2x^(2))+(1)/(2x)]+(1)/(6)int (e^(x))/(x)dx .

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

int(e^((x)/(2))-1)^(3)e^((x)/(2))dx