Using partial fractions find the integral of (15-17x)/((2+x) (1-3x)^2 )
First seperate the function into the form A/(2+x) + B/(1-3x) + C/(1-3x)2 . Find A B and C by equating the intergral to {A(1-3x)2 +B(1-3x)(2+x) +C(2+x)}/(2+x)(1-3x)2 . Cancelling the denominators gives an equation equal to 15-7x, and in terms of A, B and C. We then use comparison of the right and left hand sides to find A, B and C. By subsituting x=-2, x=1/3 and by comparing coefficients of x2 the values of A B and C can be found. Subbing these into the partial fraction equation(1st line) we can then intergrate this expression, using the fact that the intergral of 1/x is equal to ln(x).
