Evaluate the Integral integral of 16x with respect to x

Problem

(∫_^)(16*x*d(x))

Solution

1. Identify the constant factor in the integrand.

2. Apply the constant multiple rule for integration by moving the constant 16 outside the integral sign.

(∫_^)(16*x*d(x))=16*(∫_^)(x*d(x))

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

16*(∫_^)(x1*d(x))=16⋅(x(1+1))/(1+1)

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

16⋅(x2)/2

5. Divide the constant 16 by 2 and add the constant of integration C

8*x2+C

Final Answer

(∫_^)(16*x*d(x))=8*x2+C

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