Evaluate the Integral integral of 4x with respect to x

Problem

(∫_^)(4*x*d(x))

Solution

1. Identify the constant factor in the integrand.

2. Apply the constant multiple rule for integration by moving the 4 outside the integral sign.

(∫_^)(4*x*d(x))=4*(∫_^)(x*d(x))

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

4*(∫_^)(x1*d(x))=4⋅(x(1+1))/(1+1)

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

4⋅(x2)/2

5. Reduce the fraction by dividing 4 by 2

2*x2

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

2*x2+C

Final Answer

(∫_^)(4*x*d(x))=2*x2+C

Want more problems? Check here!