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laplace transform cos^2(t)

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

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∫ sin⁶(x)cos³(x)dx

Solution

sin⁷(x)7 −sin⁹(x)9 +C

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∫ sin⁶(x)cos³(x)dx

Récrire en utilisant des identités trigonométriques

=∫ (1−sin²(x))cos(x)sin⁶(x)dx

Appliquer l'intégration par subsitution: ∫ u⁶(1−u²)du

=∫ u⁶(1−u²)du

Développer u⁶(1−u²): u⁶−u⁸

=∫ u⁶−u⁸du

Appliquer la règle de la somme: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ u⁶du−∫ u⁸du

∫ u⁶du=u⁷7

∫ u⁸du=u⁹9

=u⁷7 −u⁹9

Remplacer u=sin(x)

=sin⁷(x)7 −sin⁹(x)9

Ajouter une constante à la solution

=sin⁷(x)7 −sin⁹(x)9 +C

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

laplace transform cos^2(t)

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