Find the Antiderivative f(x)=3x

Problem

(∫_^)(3*x*d(x))

Solution

1. Identify the function to be integrated, which is ƒ(x)=3*x

2. Apply the constant multiple rule for integration, which allows the constant 3 to be moved outside the integral sign.

(∫_^)(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 Here, n=1

(∫_^)(x1*d(x))=(x(1+1))/(1+1)

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

(x2)/2

5. Combine the constant and the result of the power rule, and add the constant of integration C

3⋅(x2)/2+C

Final Answer

(∫_^)(3*x*d(x))=(3*x2)/2+C

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