Introduction:
An internal coprocessor is a specialized processing unit that is integrated into a central processing unit (CPU). Its purpose is to handle specific types of calculations and tasks more efficiently than the CPU itself. In this case, we are looking for a processor that has an internal coprocessor among the given options.

Explanation:
Among the given options (8087, 80287, 80387, and 80486DX), the correct answer is option 'D' - 80486DX. Let's understand why:

8087:
- The 8087 is a math coprocessor introduced by Intel for the 8086 and 8088 processors. It is an external coprocessor and not an internal one. It needs to be physically added to the CPU socket.
- The 8087 provides additional mathematical and floating-point capabilities to the CPU, but it is not integrated into the CPU itself.

80287:
- The 80287 is also a math coprocessor, but it was designed for the 80286 processor.
- Similar to the 8087, the 80287 is an external coprocessor and not integrated into the CPU.

80387:
- The 80387 is a math coprocessor designed for the 80386 processor.
- Like its predecessors, the 80387 is an external coprocessor and needs to be physically added to the CPU socket.

80486DX:
- The 80486DX is the successor to the 80386 processor and introduced by Intel.
- Unlike the previous options, the 80486DX has an internal coprocessor.
- The internal coprocessor in the 80486DX is responsible for handling floating-point operations and mathematical calculations.
- This integration allows for faster and more efficient processing of mathematical tasks compared to using an external coprocessor.

Conclusion:
Among the given options, the processor with an internal coprocessor is the 80486DX. It is the only processor in the list that has an integrated coprocessor for handling mathematical calculations and floating-point operations.