Final answer:
The problem requires the evaluation of the integral of arctan(1/x) from 3 to 5 using integration by parts, a college-level calculus concept. The solution involves differentiating arctan(1/x) to find du and integrating dx to find v, then applying the integration by parts formula and simplifying.
Step-by-step explanation:
The student's question about evaluating the integral of arctan(1/x) from 3 to 5 falls under the subject of Mathematics, specifically integral calculus, which is typically studied in college. To solve this problem, it's important to recognize the connection between arctan and tan functions and how they relate in terms of derivatives.
Using integration by parts, where u = arctan(1/x) and dv = dx, we can determine du and v and proceed to solve the integral applying the formula ∫ u dv = uv - ∫ v du. This process requires a more than 100-level understanding of calculus concepts, as there are many steps involved in correctly applying integration techniques and manipulating the integral to achieve the correct result.
Steps to Evaluate the Integral
- Choose u = arctan(1/x) and dv = dx.
- Compute du by differentiating u and find v by integrating dv.
- Apply the integration by parts formula.
- Simplify the resulting expression and evaluate the definite integral from 3 to 5.
The related keyword in this solution is the integration technique used, which may include substitution and integration by parts in more complicated examples.