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domain of ln(x)

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

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∫ √49+x²dx

Solution

49(198 x√49+x²+12 ln(|x+√49+x²|7 ))+C

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∫ √49+x²dx

Trigonometrische Substitution anwenden: ∫ 49sec³(u)du

=∫ 49sec³(u)du

Entferne die Konstante: ∫a·f(x)dx=a·∫f(x)dx

=49· ∫ sec³(u)du

Wende integrale Reduktion an

=49(sec²(u)sin(u)2 +12 · ∫ sec(u)du)

∫ sec(u)du=ln|tan(u)+sec(u)|

=49(sec²(u)sin(u)2 +12 ln|tan(u)+sec(u)|)

Setze in u=arctan(17 x) ein

=49(sec²(arctan(17 x))sin(arctan(17 x))2 +12 ln|tan(arctan(17 x))+sec(arctan(17 x))|)

Vereinfache 49(sec²(arctan(17 x))sin(arctan(17 x))2 +12 ln|tan(arctan(17 x))+sec(arctan(17 x))|): 49(198 x√49+x²+12 ln(|x+√49+x²|7 ))

=49(198 x√49+x²+12 ln(|x+√49+x²|7 ))

Füge eine Konstante zur Lösung hinzu

=49(198 x√49+x²+12 ln(|x+√49+x²|7 ))+C

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

domain of ln(x)

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