integral of picsc(x)

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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

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Steps Examples

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∫ πcsc(x)dx

Solution

πln|tan(x2 )|+C

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Solution steps

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∫ πcsc(x)dx

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

=π· ∫ csc(x)dx

Apply u-substitution: ∫ 1u du

=π· ∫ 1u du

Use the common integral: ∫ 1u du=ln(|u|)

=πln|u|

Substitute back u=tan(x2 )

=πln|tan(x2 )|

Add a constant to the solution

=πln|tan(x2 )|+C

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Notebook

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

integral of picsc(x)

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