Find the Antiderivative 6x

Problem

(∫_^)(6*x*d(x))

Solution

1. Identify the integral to be solved, which is the antiderivative of the function 6*x with respect to x

2. Apply the constant multiple rule by moving the constant factor 6 outside of the integral sign.

(∫_^)(6*x*d(x))=6*(∫_^)(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

6*(∫_^)(x1*d(x))=6⋅(x(1+1))/(1+1)+C

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

6⋅(x2)/2+C

5. Reduce the fraction by dividing 6 by 2

3*x2+C

Final Answer

(∫_^)(6*x*d(x))=3*x2+C

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