Evaluate the Integral integral of (y-1)^7 with respect to y

Problem

(∫_^)((y−1)7*d(y))

Solution

1. Identify the integral as a power of a linear expression, which can be solved using a simple usubstitution.

2. Substitute u=y−1 which implies that d(u)=d(y)

3. Rewrite the integral in terms of u

(∫_^)(u7*d(u))

4. Apply the power rule for integration, which states that (∫_^)(un*d(u))=(u(n+1))/(n+1)+C

(u8)/8+C

5. Back-substitute the original expression y−1 for u to get the final result.

Final Answer

(∫_^)((y−1)7*d(y))=((y−1)8)/8+C

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