Use the reduction formulas in a table of integrals to evaluate the following integrals. int p^2e^{-3p}dp

Kaycee Roche 2020-12-25 Answered
Use the reduction formulas in a table of integrals to evaluate the following integrals.
p2e3pdp
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Expert Answer

grbavit
Answered 2020-12-26 Author has 109 answers
Reduction formula for Exponential function is given as:
xaebxdx=[1bxaebx][abxa1ebc]dx
we have to evaluate:
p2e3pdp
Using reduction formula, we will integrate it.
p2e3pdp=[13p2e3p][23p21e3p]dp
=13p2e3p+23pe3pdp
Now, we will integratepe3pdp using integration by parts
pe3pdp=pe3pdp[ddx(p)e3pdp]dp
=pe3p3[1e3p3]dp
=pe3p3+13e3pdp
=pe3p3+13e3p3+c
=pe3p319e3p+c
Putting above integration value in equation, we get 
p2e3pdp=13p2e3p+23[pe3p319e3p]+c
=13p2e3p29pe3p227e3p+c
=e3p(13p2+29+227)+c
Hence, this is required integration.
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