Question

integral of (x^2+1)/(2x)dx from 1 to 2

Answer 1

Hiint :-
\(\dfrac{x^2+1}{2x}=\dfrac{ 1}{2x}+\dfrac{x^2 }{2x}\)

Answer 2

\[\int_1^2\frac{x^2+1}{2x}\,\mathrm dx\\
=\frac12\int_1^2\frac{x^2+1}{x}\,\mathrm dx\\
=\frac12\left(\int_1^2\frac{x^2}{x}\,\mathrm dx+\int_1^2\frac{1}{x}\,\mathrm dx\right)\\
=\frac12\left(\int_1^2x\,\mathrm dx+\int_1^2\frac{1}{x}\,\mathrm dx\right)\\=\]