1. The problem is to solve an integral using integration by parts. 2. The formula for integration by parts is: $$\int u\,dv = uv - \int v\,du$$ where $u$ and $dv$ are parts of the original integral chosen to simplify the problem. 3. Choose $u$ and $dv$ from the integral such that differentiating $u$ and integrating $dv$ simplifies the integral. 4. Compute $du$ by differentiating $u$ and compute $v$ by integrating $dv$. 5. Substitute into the formula and simplify the resulting integral. 6. If the resulting integral is simpler, evaluate it; otherwise, repeat integration by parts as needed. 7. Always check your final answer by differentiating it to see if you get the original integrand.