Interesting Maths Q11 (Easy)

Int [(ax+b)/(cx+d)] dx
= Int [ax/(cx+d) + b/(cx+d)] dx
= (a/c) Int [x/(x+d/c)] dx + (b/c) Int [1/(x+d/c)] dx
= (a/c) Int {1 - [(d/c)/(x+d/c)]} dx + (b/c) Int [1/(x+d/c)] dx
= (a/c) Int [1] dx - (a/c)(d/c) Int[1/(x+d/c)] dx + (b/c)ln (x+d/c) + K where K is a constant
= (a/c)x - (ad/c^2)ln(x+d/c) + (b/c)ln (x+d/c) + M where M is a constant
= (a/c)x - (ad/c^2 + b/c)ln(x+d/c) + M
= (a/c)x - [(ad + bc)/c^2]ln(x+d/c) + M

OxO


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[(bc-ad)log(cx+d)+acx]/(c^2)+C or another expression ?