Find the Antiderivative 5x

Problem

(∫_^)(5*x*d(x))

Solution

1. Identify the integral as a power rule problem where the function is 5*x1

2. Apply the constant multiple rule by moving the constant 5 outside the integral sign.

5*(∫_^)(x*d(x))

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

5⋅(x(1+1))/(1+1)

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

(5*x2)/2

5. Add the constant of integration C to represent the family of all possible antiderivatives.

(5*x2)/2+C

Final Answer

(∫_^)(5*x*d(x))=(5*x2)/2+C

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