Engineering Board Exam Reviewer · Integration by Parts · medium

Evaluate: e2 x ≤ft(3 x ),dx

1. ≤ft(2 ≤ft(3 x ) + 3 ≤ft(3 x ) ) e2 x13+C
2. ≤ft(3 ≤ft(3 x ) - 2 ≤ft(3 x ) ) e2 x13+C
3. ≤ft(2 ≤ft(3 x ) - 3 ≤ft(3 x ) ) e2 x13+C
4. ≤ft(2 ≤ft(3 x ) - 3 ≤ft(3 x ) ) e2 x5+C

Answer

C. ≤ft(2 ≤ft(3 x ) - 3 ≤ft(3 x ) ) e2 x13+C

Solution

Parts twice gives I= e2x 3x2- 3e2x 3x4- 94I. Solving, 13/4I= e2x(2 3x-3 3x)4, so I= e2x(2 3x-3 3x)13+C.

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