integral of (x^3)/(x^4+1)

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

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

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∫ x³x⁴+1 dx

Solution

14 ln|x⁴+1|+C

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∫ x³x⁴+1 dx

Apply u-substitution: ∫ 14u du

=∫ 14u du

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=14 · ∫ 1u du

Use the common integral: ∫ 1u du=ln(|u|)

=14 ln|u|

Substitute back u=x⁴+1

=14 ln|x⁴+1|

Add a constant to the solution

=14 ln|x⁴+1|+C

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integral of (x^3)/(x^4+1)

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integral of (x^3)/(x^4+1)

Solution

Solution steps

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