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Evaluate the following: intx^3e^xdx...

Evaluate the following:
`intx^3e^xdx`

Text Solution

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`intx^3e^xdx=x^3e^x-int3x^2e^xdx`
=`x^3e^x-3{x^2e^x-int2xe^xdx`
=`x^3e^x-3x^2e^x+6intxe^xdx`
=`x^3e^x-3x^2e^x+6{x.e^x-int1.e^xdx}`
=`x^3e^x-3x^2e^x+6xe^x-6e^x+C`
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