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

Integration of rational functions int(x^(3)+3)/((x+1)(x^(2)+1))dx.

int(2x+3)/((x-1)(x^(2)+1))dx=log_(e){(x-1)^((5)/(2))(x^(2)+1)^(a)-(1)/(2)tan^(-1)x+C,x>1 where C is any arbitrary constant,then the value of a'a' is

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

int(2x+3)/((x-1)(x^2+1))dx =log_e{(x-1)^(5/2)(x^2+1)^a-1/2 tan^-1 x+C,x > 1 where C is any arbitrary constant, then the value of ' a' is

int(2x+3)/((x-1)(x^2+1))dx =log_e{(x-1)^(5/2)(x^2+1)^a}-1/2 tan^-1 x+C,x > 1 where C is any arbitrary constant, then the value of ' a' is

Evaluate : (i) int(3x^(2))/((1+x^(6)))dx (ii) int(x^(3))/((x^(2)+1)^(3))dx (iii) (x^(8))/((1-x^(3))^(1//3))dx

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

int(2x^(2)+3)sqrt(x+2)dx( ii) int(x^(2)+3x+1)/((x+1)^(2))dx

Evaluate: int(x^(2)+3x+1)/((x+1)^(2))dx