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points of d'intersection log_{7}(7x)

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

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fractions partielles ∫₀¹32x²−64 dx

Solution

2(ln(7)−2ln(3))

Decimal

−0.50262…

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∫₀¹32x²−64 dx

Extraire la constante: ∫a·f(x)dx=a·∫f(x)dx

=32· ∫₀¹1x²−64 dx

Prendre la fraction partielle de 1x²−64 : −116(x+8) +116(x−8)

=32· ∫₀¹−116(x+8) +116(x−8) dx

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

=32(−∫₀¹116(x+8) dx+∫₀¹116(x−8) dx)

∫₀¹116(x+8) dx=116 (2ln(3)−3ln(2))

∫₀¹116(x−8) dx=116 (ln(7)−3ln(2))

=32(−116 (2ln(3)−3ln(2))+116 (ln(7)−3ln(2)))

Simplifier 32(−116 (2ln(3)−3ln(2))+116 (ln(7)−3ln(2))): 2(ln(7)−2ln(3))

=2(ln(7)−2ln(3))

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

points of d'intersection log_{7}(7x)

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