Question

For \[\int\frac{px+q}{ax^2+bx+c}\,dx\], how is \[px+q\] written in relation to the derivative of the denominator?

Options

• \[px+q=A(x^2+a^2)+B\]

• \[px+q=A(ax^2+bx+c)+B\]

• \[px+q=A(2ax-b)+B\]

• \[px+q=A(2ax+b)+B\]

Answer 1

Since \[\frac{d}{dx}(ax^2+bx+c)=2ax+b\], the numerator is written as \[A(2ax+b)+B\]. The integral can then be split into simpler standard integrals.