Final answer:
To evaluate the integral ∫ (25 + 2²)³-dx, substitute u = 25 + 2² and simplify using the power rule of integration.
Step-by-step explanation:
To evaluate the integral ∫ (25 + 2²)³-dx, we can substitute u = 25 + 2². Taking the derivative of u with respect to x, we get du = 4xdx. Rearranging, we have dx = du / (4x).
Substituting these into the integral, we get ∫1/√u^3 * (du / (4x)).
Simplifying further, we have ∫(1/4x) * u^(-3/2)du.
This can be solved using the power rule of integration, which gives us (1/2) * u^(-1/2) + C.
Substituting back u = 25 + 2², we get the final answer as (1/2)(25 + 2²)^(-1/2) + C.