Final answer:
To evaluate the integral, a substitution can simplify the expression, and after integration, the constant of integration 'C' is added.
Step-by-step explanation:
Evaluating an Integral
The student has asked to evaluate the following integral:
∫ x⁴ √(x² - 3) dx,
where 'C' is used for the constant of integration. To properly evaluate this integral, one would typically look for a substitution that simplifies the integral or leverage integration by parts if necessary. In this case, a substitution of 'u' for 'x² - 3' could be a starting point, as it simplifies the integral to:
∫ (u + 3)² √(u) (1/2)du,
after adjusting for 'dx'. Following the integration, we add the constant 'C' to represent the constant of integration. This method is aligned with the principle of reducing an integral to a more manageable form, as discussed in example 7.4