limit as x approaches infinity of (ln(x))/(sqrt(x))

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

simplify solve for expand factor rationalize

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Steps Examples

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∫ x²−6x+8x−4 dx

Solution

2x+12 (x−4)²−8+C

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Solution steps

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∫ x²−6x+8x−4 dx

Expand x²−6x+8x−4 : x²x−4 −6xx−4 +8x−4

Apply the Sum Rule: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ x²x−4 dx−∫ 6xx−4 dx+∫ 8x−4 dx

∫ x²x−4 dx=(x−4)²2 +8(x−4)+16ln|x−4|

∫ 6xx−4 dx=6(x−4+4ln|x−4|)

∫ 8x−4 dx=8ln|x−4|

=(x−4)²2 +8(x−4)+16ln|x−4|−6(x−4+4ln|x−4|)+8ln|x−4|

Simplify (x−4)²2 +8(x−4)+16ln|x−4|−6(x−4+4ln|x−4|)+8ln|x−4|: 2x+12 (x−4)²−8

=2x+12 (x−4)²−8

Add a constant to the solution

=2x+12 (x−4)²−8+C

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