Evaluate the Integral integral of 12x with respect to x

Problem

(∫_^)(12*x*d(x))

Solution

1. Identify the constant factor in the integrand and move it outside the integral.

(∫_^)(12*x*d(x))=12*(∫_^)(x*d(x))

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

12*(∫_^)(x1*d(x))=12⋅(x(1+1))/(1+1)

3. Simplify the expression by performing the arithmetic in the exponent and the denominator.

12⋅(x2)/2

4. Divide the constant coefficient by the denominator and add the constant of integration C

6*x2+C

Final Answer

(∫_^)(12*x*d(x))=6*x2+C

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