How do you do this question?

C) 5 sin⁻¹(x − 1) + C

Step-by-step explanation:

∫ 10 / √(8x − 4x²) dx

Simplify.

∫ 5 / √(2x − x²) dx

Complete the square.

∫ 5 / √(-(x² − 2x) dx

∫ 5 / √(-(x² − 2x + 1 − 1) dx

∫ 5 / √(-(x² − 2x + 1) + 1) dx

∫ 5 / √(-(x − 1)² + 1) dx

∫ 5 / √(1 − (x − 1)²) dx

Integrate using a table.

5 sin⁻¹(x − 1) + C

d. 8

step-by-step explanation:

the given radical expression is:

we can rewrite this as:

we express as square numbers to get;

the exponents will now cancel out to give.

the correct answer is d