Dick said:I don't think it needs integration by parts. I'd do a simple u substitution. u=r^2+4, like AnnieF suggested. What 'issues' were you running into?
The formula for integrating by parts is ∫u dv = uv - ∫v du, where u and v are functions of x and dv and du are their respective derivatives.
A common method is to choose u as the part of the integrand that becomes simpler after taking the derivative, and dv as the part that becomes more complicated after being integrated.
To solve this integral using integration by parts, you would assign u = r^3 and dv = (4+r^2)^(-1/2) dr, then use the formula ∫u dv = uv - ∫v du to find the solution.
The purpose of integration by parts is to simplify a complex integral by breaking it down into smaller, more manageable parts and applying the formula to find the solution.
While integration by parts can be used for a wide range of integrals, it may not always be the most efficient method. It is important to consider other integration techniques, such as substitution or partial fractions, before deciding to use integration by parts.