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limit as x approaches infinity of (4x-7)/(x^2+5x)

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

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∫ sin(5x)dx

Solution

−15 cos(5x)+C

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Solution steps

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∫ sin(5x)dx

فعّل طريقة التكامل بالتعويض: ∫ sin(u)15 du

=∫ sin(u)15 du

∫a·f(x)dx=a·∫f(x)dx :قم بإخراج الثابت

=15 · ∫ sin(u)du

∫ sin(u)du=−cos(u) :استخدم التكامل البسيط

=15 (−cos(u))

u=5x استبدل مجددًا

=15 (−cos(5x))

بسّط

=−15 cos(5x)

أضف ثابت التكامل للحل

=−15 cos(5x)+C

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

limit as x approaches infinity of (4x-7)/(x^2+5x)

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