Evaluate the Integral integral of 3x with respect to x

Problem

(∫_^)(3*x*d(x))

Solution

1. Identify the constant and the variable part of the integrand.

2. Apply the constant multiple rule for integration by moving the constant 3 outside the integral.

(∫_^)(3*x*d(x))=3*(∫_^)(x*d(x))

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

3*(∫_^)(x1*d(x))=3⋅(x(1+1))/(1+1)

4. Simplify the expression and add the constant of integration C

3⋅(x2)/2+C

(3*x2)/2+C

Final Answer

(∫_^)(3*x*d(x))=(3*x2)/2+C

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