Find the Integral 2x

Problem

(∫_^)(2*x*d(x))

Solution

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

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

2*(∫_^)(x*d(x))

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

2⋅(x^(1+1))/(1+1)

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

2⋅(x^2)/2

5. Cancel the common factor of 2 and add the constant of integration C

x^2+C

Final Answer

(∫_^)(2*x*d(x))=x^2+C

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