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sum from x=1 to infinity of sin((npi)/2)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

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∫ sec⁴(θ)tan²(θ)dθ

Solution

tan³(θ)3 +tan⁵(θ)5 +C

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∫ sec⁴(θ)tan²(θ)dθ

Re-escribir usando identidades trigonométricas

=∫ (1+tan²(θ))sec²(θ)tan²(θ)dθ

Aplicar integración por sustitución: ∫ u²(1+u²)du

=∫ u²(1+u²)du

Expandir u²(1+u²): u²+u⁴

=∫ u²+u⁴du

Aplicar la regla de la suma: ∫f(x)±g(x)dx=∫f(x)dx±∫g(x)dx

=∫ u²du+∫ u⁴du

∫ u²du=u³3

∫ u⁴du=u⁵5

=u³3 +u⁵5

Sustituir en la ecuación u=tan(θ)

=tan³(θ)3 +tan⁵(θ)5

Agregar una constante a la solución

=tan³(θ)3 +tan⁵(θ)5 +C

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

sum from x=1 to infinity of sin((npi)/2)

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