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integral of cos^3(t)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
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∫ (x²+x)e^(−2x+1)dx

Solution

e(−12 e^−2xx²−e^−2xx−12 e^−2x)+C

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∫ (x²+x)e^−2x+1dx

(x²+x)e^−2x+1=e¹(x²+x)e^−2x

=∫ e¹(x²+x)e^−2xdx

Remover a constante: ∫a·f(x)dx=a·∫f(x)dx

=e¹· ∫ (x²+x)e^−2xdx

Simplificar

=e· ∫ (x²+x)e^−2xdx

Aplicar integração por partes: −12 e^−2x(x²+x)−∫ −e^−2xx−12 e^−2xdx

=e(−12 e^−2x(x²+x)−∫ −e^−2xx−12 e^−2xdx)

∫ −e^−2xx−12 e^−2xdx=12 e^−2xx+12 e^−2x

=e(−12 e^−2x(x²+x)−(12 e^−2xx+12 e^−2x))

Expandir −12 e^−2x(x²+x)−(12 e^−2xx+12 e^−2x): −12 e^−2xx²−e^−2xx−12 e^−2x

=e(−12 e^−2xx²−e^−2xx−12 e^−2x)

Adicionar uma constante à solução

=e(−12 e^−2xx²−e^−2xx−12 e^−2x)+C

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

integral of cos^3(t)

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integral of cos^3(t)

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