Find the Integral 4x

Problem

(∫_^)(4*x*d(x))

Solution

1. Identify the integral as a power rule problem where the function is 4*x1

2. Apply the constant multiple rule by moving the constant 4 outside the integral sign.

(∫_^)(4*x*d(x))=4*(∫_^)(x*d(x))

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

4*(∫_^)(x1*d(x))=4⋅(x(1+1))/(1+1)

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

4⋅(x2)/2

5. Reduce the fraction by dividing 4 by 2 and add the constant of integration C

2*x2+C

Final Answer

(∫_^)(4*x*d(x))=2*x2+C

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