Find the Antiderivative 5x^2

Problem

(∫_^)(5*x2*d(x))

Solution

1. Identify the integral as a power rule problem where the constant multiple can be moved outside the integral.

(∫_^)(5*x2*d(x))=5*(∫_^)(x2*d(x))

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

(∫_^)(x2*d(x))=(x(2+1))/(2+1)

3. Simplify the exponent and the denominator.

(x(2+1))/(2+1)=(x3)/3

4. Multiply by the constant factor and add the constant of integration C

5⋅(x3)/3+C=(5*x3)/3+C

Final Answer

(∫_^)(5*x2*d(x))=(5*x3)/3+C

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