Evaluate the Integral integral of 3x^2 with respect to x

Problem

(∫_^)(3*x2*d(x))

Solution

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

2. Apply the constant multiple rule by moving the constant 3 outside the integral.

(∫_^)(3*x2*d(x))=3*(∫_^)(x2*d(x))

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

3*(∫_^)(x2*d(x))=3⋅(x(2+1))/(2+1)+C

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

3⋅(x3)/3+C

5. Cancel the common factor of 3 in the numerator and denominator.

x3+C

Final Answer

(∫_^)(3*x2*d(x))=x3+C

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