Evaluate the Integral integral of 9x with respect to x

Problem

(∫_^)(9*x*d(x))

Solution

1. Identify the constant and the variable part of the integrand. The constant is 9 and the variable part is x

2. Apply the constant multiple rule for integration, which allows the constant to be moved outside the integral sign.

(∫_^)(9*x*d(x))=9*(∫_^)(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

9*(∫_^)(x1*d(x))=9⋅(x(1+1))/(1+1)

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

9⋅(x2)/2

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

(9*x2)/2+C

Final Answer

(∫_^)(9*x*d(x))=(9*x2)/2+C

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