Find the Integral 3x

Problem

(∫_^)(3*x*d(x))

Solution

1. Identify the integral as a power rule problem where the constant multiple 3 can be moved outside the integral.

(∫_^)(3*x*d(x))=3*(∫_^)(x1*d(x))

2. 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)+C

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

3⋅(x2)/2+C

4. Combine the constant and the fraction to reach the final form.

(3*x2)/2+C

Final Answer

(∫_^)(3*x*d(x))=(3*x2)/2+C

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