intercepts of (x^2+2x-1)*(2x^2-3x+6)

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

☐²

x^☐

√☐

^□√☐

□□

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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laplace transform x3^x

Solution

1(s−ln(3))²

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Solution steps

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∫ cos⁵(x)sin²(x)dx

Rewrite using trig identities

=∫ (1−sin²(x))²cos(x)sin²(x)dx

Apply u-substitution: ∫ u²(1−u²)²du

=∫ u²(1−u²)²du

Expand u²(1−u²)²: u²−2u⁴+u⁶

=∫ u²−2u⁴+u⁶du

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

=∫ u²du−∫ 2u⁴du+∫ u⁶du

∫ u²du=u³3

∫ 2u⁴du=2u⁵5

∫ u⁶du=u⁷7

=u³3 −2u⁵5 +u⁷7

Substitute back u=sin(x)

=sin³(x)3 −2sin⁵(x)5 +sin⁷(x)7

Add a constant to the solution

=sin³(x)3 −2sin⁵(x)5 +sin⁷(x)7 +C

Verify Result

=sin³(x)3 −2sin⁵(x)5 +sin⁷(x)7 +C

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inverse laplace x3^x

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

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intercepts of (x^2+2x-1)*(2x^2-3x+6)

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intercepts of (x^2+2x-1)*(2x^2-3x+6)

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