## To find the integral of the function xe^(4x^2), you correctly recognized that it is a u-substitution problem.

1. Start by letting u = 4x^2

This means du = 8x dx (taking the derivative of u with respect to x)

2. Rewrite the integral in terms of u and du.

The integral becomes: âˆ« (1/8)e^u du

3. Integrate e^u with respect to u.

The integral of e^u is simply e^u. So, we get: (1/8)e^u

4. Substitute back u with 4x^2.

Replace the u with 4x^2 in the previous result: (1/8)e^(4x^2)

5. Include the constant of integration (C).

Finally, add the constant of integration to the result from step 4: (1/8)e^(4x^2) + C

Therefore, the integral of xe^(4x^2) is (1/8)e^(4x^2) + C, where C is the constant of integration.