Calculate the following definite integrals:

Question

(a)∫1/x^3−x dx
(b)∫2 −x/x^2+ x dx
(c)∫sin(x)/1 −cos^2(x) dx

Answer 1

the above are not definite integrals
(a) assuming the usual carelessness with parentheses (otherwise it's just the power rule)
∫ 1/(x^3-x) dx = ∫1/(x*x-1)(x+1)) dx
use partial fractions

(b) ∫(2-x)/(x^2+x) dx = ∫(2-x)/(x(x+1)) dx
use partial fractions

(c) ∫sinx/(1-cos^2x) dx ∫sinx/sin^2x dx = ∫cscx dx
standard trig integral

post your work if you get stuck