Determine whether the following statements are true and give an explanation or counterexample.

a. The integral ∫ x²e^2x dx can be evaluated using integration by parts.

b. To evaluate the integral analytically, it is best to use partial fractions.

c. One computer algebra system produces ∫ 2 sin x cos x dx = sin² x. Another computer algebra system produces ∫ 2 sin x cos x dx = -cos² x. One computer algebra system is wrong (apart from a missing constant of integration).

d. ∫ 2 sin x cos x dx = -1/2 cos 2x + C.

e. The best approach to evaluating is to use the change of variables u = x³ + 1.

Transcribed Image Text:

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