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

Problem

(∫_^)(2*x−3*x2*d(x))

Solution

1. Apply the sum rule for integration, which allows the integral of a sum to be split into the sum of the integrals.

(∫_^)(2*x−3*x2*d(x))=(∫_^)(2*x*d(x))−(∫_^)(3*x2*d(x))

2. Apply the constant multiple rule to move the coefficients outside of the integral signs.

2*(∫_^)(x*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

2(x2)/2−3(x3)/3+C

4. Simplify the expression by canceling the common factors in the numerators and denominators.

x2−x3+C

Final Answer

(∫_^)(2*x−3*x2*d(x))=x2−x3+C

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