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Question Number 11621 by Nayon last updated on 29/Mar/17
Evaluate ∫((ax+b)/(cx+d))dx
Evaluate∫ax+bcx+ddx
Answered by mrW1 last updated on 29/Mar/17
=∫(((a/c)(cx+d)+(b−((ad)/c)))/(cx+d))dx =(a/c)∫dx+(b−((ad)/c))×(1/c)∫((d(cx+d))/(cx+d)) =((ax)/c)+((bc−ad)/c^2 )×ln (cx+d)+C
=∫ac(cx+d)+(b−adc)cx+ddx=ac∫dx+(b−adc)×1c∫d(cx+d)cx+d=axc+bc−adc2×ln(cx+d)+C

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