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RECOGNIZING INTEGRALS Name___________________________ Although the integrals in each group below have similarities, they require different approaches. For each integral decide which of the following is needed: 1) substitution, 2) algebra or a trig identity, 3) nothing needed, or 4) can’t be done by the techniques in Calculus I. Then evaluate each integral (except for the 4th type of course). 1. A. B. x 3 1 dx 2 3 x x 1 dx 4 C. D. x x3 1dx 3 1 dx 2 2. A. e x2 dx 3. A. x 1 x 2 dx 1 x 2 dx B. ex 3 e x dx B. C. e C. D. D. x 3 dx ln e2 x x 2 dx 1 1 x2 xdx 1 x2 dx cos 4 dx 5. A. B. 1 cos 2 xdx B. cos C. cos x dx sin x C. tan x cos xdx D. D. tan x 1 4. A. cos x dx sin x tan(3x) sec(3x)dx dx 2 x dx