SOLUTION Notice that t 2 becomes simpler when differentiated (whereas e 5 t is m

Question

SOLUTIONNotice thatt2becomes simpler when differentiated (wherease5tis mostly unchanged when differentiated or integrated), so we choose

Thendu=

u = dv= dt Then du =dt v= Find t^2e^5tdt. SOLUTION Notice that t^2becomes simpler when differentiated (whereas e^5t is mostly unchanged when differentiated or integrated), so we choose Integration by parts gives The integral that we obtained, te^5t dt, is simpler than the original integral but is still not obvious. Therefore, we use integration by parts a second time, this time withu=tanddv=e^5tdt. Thendu= Putting this in Equation 3, we get

Explanation / Answer

t*T e^(5t)/5 - (2/5)[ te^(5t)/5 - e^(5t)/25 ] t*t e^(5t)/5 - (2/25) te^(5t) + 2/125 e^(5t) ]

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