integral of (e^x)/(1+e^{2x)}

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

simplify solve for inverse tangent line

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∫ e^x1+e^2x dx

Solution

arctan(e^x)+C

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Solution steps

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∫ e^x1+e^2x dx

Apply u-substitution: ∫ 11+u² du

=∫ 11+u² du

Use the common integral: ∫ 11+u² du=arctan(u)

=arctan(u)

Substitute back u=e^x

=arctan(e^x)

Add a constant to the solution

=arctan(e^x)+C

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

integral of (e^x)/(1+e^{2x)}

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