Evaluate the Integral integral of 5x with respect to x

Problem

(∫_^)(5*x*d(x))

Solution

1. Identify the constant factor in the integrand.

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

(∫_^)(5*x*d(x))=5*(∫_^)(x*d(x))

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

4. Substitute n=1 into the power rule formula.

5*(∫_^)(x1*d(x))=5⋅(x(1+1))/(1+1)+C

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

5⋅(x2)/2+C=(5*x2)/2+C

Final Answer

(∫_^)(5*x*d(x))=(5*x2)/2+C

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