Question

Write down an integral that can be solved with integration by parts by choosing $u$to be the entire integrand and$dv=dx$.

Short answer

The integral which can be solved with integration by parts by choosing $u$to be the entire integrand and $dv=dx$is $\int \ln xdx$

Step-by-step solution

Step 1. Given information 

Here, we are asked to find an integral in which we can choose $u$to be the entire integrand and $dv=dx$while solving the integral using integration by parts.

Step 2. Concept

If $u$and $v$are differentiable functions, then the formula for integration by parts is$\int udv=uv-\int vdu$

Step 3. Finding the integral

Consider the integrand to be $\ln x$.

Then, in the integral $\int \ln xdx$, we will be considering $u=\ln x$which is the integrand and$dv=dx$while solving the integral using integration by parts.