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integral of cos(3t)

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

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ddx

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

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ddx (e^2x)

Solution

e^2x· 2

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Taylor Series

Taylor series of function f(x) at a is defined as:
f(x)=f(a)+f^′(a)1! (x−a)+f^′′(a)2! (x−a)²+f^′′′(a)3! (x−a)³+…

Apply the Taylor Formula

=−1+ddx (x(1−2x ))(1)1! (x−1)+d²dx² (x(1−2x ))(1)2! (x−1)²+d³dx³ (x(1−2x ))(1)3! (x−1)³+…

Evaluate Derivatives

=−1+11! (x−1)+02! (x−1)²+03! (x−1)³+04! (x−1)⁴+05! (x−1)⁵+06! (x−1)⁶+07! (x−1)⁷+08! (x−1)⁸+09! (x−1)⁹+010! (x−1)¹⁰

Refine

=−1+(x−1)

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

integral of cos(3t)

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