Find the Antiderivative 9x^2

Problem

(∫_^)(9*x2*d(x))

Solution

1. Identify the integral as a power rule problem, where the function is of the form a*xn

2. Apply the constant multiple rule by moving the constant 9 outside the integral.

(∫_^)(9*x2*d(x))=9*(∫_^)(x2*d(x))

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

9*(∫_^)(x2*d(x))=9⋅(x(2+1))/(2+1)+C

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

9⋅(x3)/3+C

5. Divide the constant 9 by 3 to reach the final simplified form.

3*x3+C

Final Answer

(∫_^)(9*x2*d(x))=3*x3+C

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