range of (x-1)^3

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

☐²

x^☐

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log_□

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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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∫ x⁴−x²+2x²(x−1) dx

Solution

x²2 +x−2ln|x|+2x +2ln|x−1|+C

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Solution steps

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∫ x⁴−x²+2x²(x−1) dx

Take the partial fraction of x⁴−x²+2x²(x−1) : x+1−2x −2x² +2x−1

=∫ x+1−2x −2x² +2x−1 dx

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

=∫ xdx+∫ 1dx−∫ 2x dx−∫ 2x² dx+∫ 2x−1 dx

∫ xdx=x²2

∫ 1dx=x

∫ 2x dx=2ln|x|

∫ 2x² dx=−2x

∫ 2x−1 dx=2ln|x−1|

=x²2 +x−2ln|x|−(−2x )+2ln|x−1|

Simplify

=x²2 +x−2ln|x|+2x +2ln|x−1|

Add a constant to the solution

=x²2 +x−2ln|x|+2x +2ln|x−1|+C

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