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vertices (x+5)^2

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

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log_□

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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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∫ tan³(x)sec⁴(x)dx

Solution

tan⁴(x)4 +tan⁶(x)6 +C

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∫ tan³(x)sec⁴(x)dx

Перепишите используя тригонометрические тождества

=∫ (1+tan²(x))sec²(x)tan³(x)dx

Применить подстановку интеграла: ∫ u³(1+u²)du

=∫ u³(1+u²)du

Расширить u³(1+u²): u³+u⁵

=∫ u³+u⁵du

Применить правило суммы: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ u³du+∫ u⁵du

∫ u³du=u⁴4

∫ u⁵du=u⁶6

=u⁴4 +u⁶6

Делаем обратную замену u=tan(x)

=tan⁴(x)4 +tan⁶(x)6

Добавить константу к решению

=tan⁴(x)4 +tan⁶(x)6 +C

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Notebook

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

vertices (x+5)^2

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