To integrate $\int \dfrac{px+q}{ax^2+bx+c}\,dx$, one writes $px+q=A\df…

Question

To integrate $\int \dfrac{px+q}{ax^2+bx+c}\,dx$, one writes $px+q=A\dfrac{d}{dx}(ax^2+bx+c)+B$. This equals

Accepted Answer

A. $A(2ax+b)+B$

1. The derivative $\dfrac{d}{dx}(ax^2+bx+c)=2ax+b$.
2. Hence $px+q=A(2ax+b)+B$.
3. $A$ and $B$ are then fixed by comparing $x$-coefficients and constants.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.309_

Answer

$A(ax^2+bx+c)+B$

Answer

$A(2ax)+B$

Answer

$A(ax+b)+B$