Find the Integral 2x+1

Problem

(∫_^)(2*x+1*d(x))

Solution

1. Identify the integral as a sum of two separate terms using the linearity property of integration.

(∫_^)(2*x+1*d(x))=(∫_^)(2*x*d(x))+(∫_^)(1*d(x))

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

(∫_^)(2*x*d(x))=2⋅(x2)/2=x2

3. Integrate the constant term, noting that the integral of a constant k is k*x

(∫_^)(1*d(x))=x

4. Combine the results and add the constant of integration C

x2+x+C

Final Answer

(∫_^)(2*x+1*d(x))=x2+x+C

Want more problems? Check here!