`int (x^2-1)/(x^3+x) dx` Use partial fractions to find the indefinite integral

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Now let's create partial fraction template,


Multiply equation by the denominator,




Comparing the coefficients of the like terms,

`A+B=1`  ----------------(1)



Plug the value of A in equation 1,



Plug in the values of A,B and C in the partial fraction template,



Apply the sum rule,


Take the constant out,


Now evaluate both the integrals separately,


Now let's evaluate second integral,


Apply integral substitution: `u=x^2+1`





Substitute back `u=x^2+1`



Simplify and add a constant C to the solution,



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