Find the Antiderivative 3x

Problem

(∫_^)(3*x*d(x))

Solution

1. Identify the integral as a power rule problem, where the expression is of the form a*x^n

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

(∫_^)(3*x*d(x))=3*(∫_^)(x^1*d(x))

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

3*(∫_^)(x^1*d(x))=3⋅(x^(1+1))/(1+1)+C

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

3⋅(x^2)/2+C=3/2*x^2+C

Final Answer

(∫_^)(3*x*d(x))=3/2*x^2+C

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