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Question Number 170610 by Sotoberry last updated on 27/May/22

Answered by aleks041103 last updated on 27/May/22

$$IBP$$$$\int udv=uv-\int vdu$$$$u=x^2+x+1$$$$v=e^x$$$$du=(2x+1)dx$$$$dv=e^{x}dx$$$$\Rightarrow \int (x^2+x+1)e^{x}dx=(x^2+x+1)e^x-\int (2x+1)e^{x}dx$$$$againIBP$$$$u=2x+1$$$$v=e^x$$$$du=2dx$$$$dv=e^{x}dx$$$$\Rightarrow \int (2x+1)e^{x}dx=(2x+1)e^x-2\int e^{x}dx=$$$$=(2x-1)e^x+C$$$$\Rightarrow \int (x^2+x+1)e^{x}dx=(x^2-x+2)e^x+C$$

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