integral of cosh^2(x)

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

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(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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∫ cosh²(x)dx

Solution

12 (x+12 sinh(2x))+C

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∫ cosh²(x)dx

Rewrite using trig identities

=∫ 1+cosh(2x)2 dx

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

=12 · ∫ 1+cosh(2x)dx

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=12 (∫ 1dx+∫ cosh(2x)dx)

∫ 1dx=x

∫ cosh(2x)dx=12 sinh(2x)

=12 (x+12 sinh(2x))

Add a constant to the solution

=12 (x+12 sinh(2x))+C

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

integral of cosh^2(x)

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