Y9gain 704 31.) Se Sine dx Chapter 8. Integration Techniques 8.2.31 Let u = e2x and du = er sin er dr Then du = 2r dx and v = - cos e. Then we have 2e e3a sin et d.x = p2x cos e" + 2 e20 cos e" dr. To compute the last integral, we let u = e and dv = the last integral is et cos e" dx. Then du = e dx and v = sin e". Then e2* cos e" dx = 2e" sin et -2 e" sin e" dx = 2e" sin e" + 2 cos e + C. Combining these results gives a final answer of 3x sin e" dx = e2 cos e +2e" sin e" + 2 cos e + C.

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