wksht_19_solutions.pdf - Worksheet 19 Solutions 2020 MATH...

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Worksheet 19 Solutions 2020 MATH 211, Week 10 Problem 1. Evaluate the following indefinite integrals. Not all problems will require the same method to compute. (a) R ln(3 x )(5 x 4 + 3 x 2 ) dx (b) R x 2 + x 4 x 3 dx (c) R xe 2 x dx (d) R 7 x 2 e - 2 x dx
(e) R x π e x π x dx (f) R ln( x ) dx Solutions:
2
To solve the second integral we integrate by parts again: u = - 7 x ; dv = e - 2 x ; v = - 1 2 e - 2 x ; du = - 7, so Z udv = uv - Z vdu = 7 x 2 e - 2 x - 7 2 Z e - 2 x = 7 x 2 e - 2 x + 7 4 e - 2 x + C and thus the answer is - 7 x 2 2 e - 2 x - 7 x 2 e - 2 x - 7 4 e - 2 x + C . (e) For this we u -substitue; letting u = x π ; du = πx π -

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