Evaluate the Integral integral of 2x with respect to x

Problem

(∫_^)(2*x*d(x))

Solution

1. Identify the integral as a power rule problem where the integrand is 2*x1

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

(∫_^)(2*x*d(x))=2*(∫_^)(x*d(x))

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

2*(∫_^)(x1*d(x))=2⋅(x(1+1))/(1+1)+C

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

2⋅(x2)/2+C

5. Cancel the common factor of 2 in the numerator and denominator.

x2+C

Final Answer

(∫_^)(2*x*d(x))=x2+C

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