Q.Evaluate : $\int (3+x)(2-5x)\,dx$.

Multiply out $(3+x)(2-5x)=6-13x-5x^2$, then integrate each term using the power rule.

Expand the integrand:

$(3+x)(2-5x)=6-15x+2x-5x^2=6-13x-5x^2.$

Integrate term by term with $\displaystyle\int x^n\,dx=\frac{x^{n+1}}{n+1}$: …