Question

Instructions : integrate the following

Answer 1

You can simplify the integrand:

`(3x^2+4x+1)/(2x)=\frac{3x}2+2+\frac1{2x}`

Then integrate term-by-term:

`\displaystyle\int(3x^2+4x+1)/(2x)\,\mathrm dx=\frac32\int x\,\mathrm dx+2\int\mathrm dx+\frac12\int\frac{\mathrm dx}x`

`=\frac{3x^2}4+2x+\frac12\ln|x|+C`