Evaluate the Integral 2 integral of x with respect to x

Problem

2*(∫_^)(x*d(x))

Solution

1. Identify the constant multiple rule for integration, which allows the constant to remain outside the integral.

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

3. Substitute n=1 into the power rule formula.

2*(∫_^)(x*d(x))=2⋅(x(1+1))/(1+1)+C

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

2*(∫_^)(x*d(x))=2⋅(x2)/2+C

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

2*(∫_^)(x*d(x))=x2+C

Final Answer

2*(∫_^)(x*d(x))=x2+C

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