Solve 2 and 4

338 Example 3.54 MAT202 Test I Fall I, 2022 1. Evaluate xe5x+2dx (15 points) 2. Evaluate (sin2x).(cos5x)dx, then check your answer by differentiating your answer with respect to x (10 points) 3. Compute [(In(Inx)-Inx)/x]dx from x=es to x=e (10 points) 4. Evaluate Jdx/sqrt(x2+4x+13) by completing the square; after trig sub, draw and label the reference triangle (5 points for this, 15 points over all) 5. Find (cos4x).(cos6x)dx (10 points) 6. Evaluate Je*dx/(e2x-6e*+8) (10 points) 7. Compute (x2+3x-44)dx/(x+3)-(x+5).(3x-2) Hint on methods: either 3 equations in 3 unknowns or strategic substitution...(15 points) 8. Consider Jxexp(-x2) x=0 to x=infinity, where exp denotes e to a function. Determine whether the integral converges (C) or diverges (D). If C determine the value, and justify if D. Use appropriate limit terminology (15 points)