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integral of (1-x)e^x

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

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∫ (1−x)e^xdx

Solution

−e^xx+2e^x+C

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∫ (1−x)e^xdx

Apply Integration By Parts: e^x(1−x)−∫ −e^xdx

=e^x(1−x)−∫ −e^xdx

∫ −e^xdx=−e^x

=e^x(1−x)−(−e^x)

Simplify e^x(1−x)−(−e^x): −e^xx+2e^x

=−e^xx+2e^x

Add a constant to the solution

=−e^xx+2e^x+C

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

integral of (1-x)e^x

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