Evaluate the Integral

Problem

(∫_^)(3*x8−7*x3+7*d(x))

Solution

1. Apply the sum rule for integration, which allows the integral of a sum to be written as the sum of the integrals.

(∫_^)(3*x8*d(x))−(∫_^)(7*x3*d(x))+(∫_^)(7*d(x))

2. Apply the power rule for integration, which states that (∫_^)(xn*d(x))=(x(n+1))/(n+1) for n≠−1

3⋅(x9)/9−7⋅(x4)/4+7*x+C

3. Simplify the coefficients by reducing the fractions where possible.

1/3*x9−7/4*x4+7*x+C

Final Answer

(∫_^)(3*x8−7*x3+7*d(x))=1/3*x9−7/4*x4+7*x+C

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