Evaluate the Integral

Problem

(∫_^)(11*(11*x−7)2*d(x))

Solution

1. Identify the structure of the integral, which is in the form (∫_^)(a*(b*x+c)n*d(x))

2. Apply the substitution method by letting u=11*x−7

3. Calculate the differential d(u) by differentiating u with respect to x which gives d(u)=11*d(x)

4. Substitute u and d(u) into the integral to transform it into (∫_^)(u2*d(u))

5. Integrate using the power rule (∫_^)(un*d(u))=(u(n+1))/(n+1)+C

6. Back-substitute the original expression for u to get the final result in terms of x

Final Answer

(∫_^)(11*(11*x−7)2*d(x))=((11*x−7)3)/3+C

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