Question

Instructions : integrate the following

Answer 1

You can simplify the integrand:

$\dfrac{3x^2+4x+1}{2x}=\dfrac{3x}2+2+\dfrac1{2x}$

Then integrate term-by-term:

$\displaystyle\int\frac{3x^2+4x+1}{2x}\,\mathrm dx=\frac32\int x\,\mathrm dx+2\int\mathrm dx+\frac12\int\frac{\mathrm dx}x$

$=\dfrac{3x^2}4+2x+\dfrac12\ln|x|+C$