Read through all the steps below carefully:

- We know from the product rule that \(\frac{d}{dx}(uv)=\frac{dv}{dx}u+\frac{du}{dx}v\).
- Integrate both sides with respect to \(x\) to get \(uv=\int u\ dv+\int\ v\ du\implies \int u\ dv=uv-\int v\ du\).
- Consider \(\int_1^2 \frac{dx}{x}\).
- Define \(u=\frac{1}{x}\) and \(dv=dx\).
- Then, \(du=-\frac{dx}{x^2}\) and \(v=x\).
- Substitute the variables into the equation in step 2 to get \(\int_1^2 \frac{dx}{x}=1+\int_1^2 \frac{dx}{x}\).
- Subtract both sides of the equation in step 6 by \(\int_1^2 \frac{dx}{x}\) to get \(0=1\).

If you enjoyed this problem, you may want to consider trying this problem.

×

Problem Loading...

Note Loading...

Set Loading...