integral of xe^{2x}

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

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≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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∫ xe^2xdx

Solution

14 (e^2x· 2x−e^2x)+C

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∫ xe^2xdx

Apply u-substitution: ∫ e^uu4 du

=∫ e^uu4 du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=14 · ∫ e^uudu

Apply Integration By Parts: e^uu−∫ e^udu

=14 (e^uu−∫ e^udu)

∫ e^udu=e^u

=14 (e^uu−e^u)

Substitute back u=2x

=14 (e^2x· 2x−e^2x)

Add a constant to the solution

=14 (e^2x· 2x−e^2x)+C

Verify Result

=14 (e^2x· 2x−e^2x)+C

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

integral of xe^{2x}

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integral of xe^{2x}

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