Evaluate the integral: (int (3x^2-2x+1)e^{x^3-x^2+x} dx)

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Step:1 ：First, let&#x27;s make a substitution. We set (u = x^3 - x^2 + x), then the differential of (u) is (du = (3x^2 - 2x + 1)dx)Step:2 ：Substitute (u) and (du) into the integral, we get (int e^u du)Step:3 ：The integral of (e^u) with respect to (u) is (e^u)Step:4 ：Substitute (u) back into the integral, we get (e^{x^3-x^2+x})

Answer

Step: 1 ：First, let&#x27;s make a substitution. We set (u = x^3 - x^2 + x), then the differential of (u) is (du = (3x^2 - 2x + 1)dx)Step: 2 ：Substitute (u) and (du) into the integral, we get (int e^u du)Step: 3 ：The integral of (e^u) with respect to (u) is (e^u)Step: 4 ：Substitute (u) back into the integral, we get (e^{x^3-x^2+x})

Evaluate the integral: \(\int (3x^2-2x+1)e^{x^3-x^2+x} dx\)

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