## Math Problem Statement

ans

## Solution

## Ask a new question for Free

### By Image

Drop file here or Click Here to upload

## Math Problem Analysis

### Mathematical Concepts

Improper Integral

Complex Analysis

Integral Calculus

### Formulas

f(a) = ∫[0, ∞] (e^(-ax) * sin(x) / x) dx

f(a) = arctan(1/a)

### Theorems

Improper Integrals Theorem

Convergence of Improper Integrals

Standard Results for Definite Integrals

### Suitable Grade Level

College Level (Advanced Calculus or Complex Analysis)

## Related Recommendation

Evaluate Improper Integral Using Double Integral and Laplace Transform

Evaluate Integrals Involving x * e^(-ax) and Trigonometric Functions

Solve the Improper Integral ∫_0^∞ f(x) dx

How to Solve the Integral of x e^(-x) from 0 to Infinity

Evaluate the Integral ∫₀^∞ e^(-3t) sin(2t) dt Using Laplace Transform