inversa -5x+e^x

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

☐²

x^☐

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ddx

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

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Steps Examples

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∫ tan⁶(x)sec⁴(x)dx

Solution

tan⁷(x)7 +tan⁹(x)9 +C

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Solution steps

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∫ tan⁶(x)sec⁴(x)dx

Re-escribir usando identidades trigonométricas

=∫ (1+tan²(x))sec²(x)tan⁶(x)dx

Aplicar integración por sustitución: ∫ u⁶(1+u²)du

=∫ u⁶(1+u²)du

Expandir u⁶(1+u²): u⁶+u⁸

=∫ u⁶+u⁸du

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

=∫ u⁶du+∫ u⁸du

∫ u⁶du=u⁷7

∫ u⁸du=u⁹9

=u⁷7 +u⁹9

Sustituir en la ecuación u=tan(x)

=tan⁷(x)7 +tan⁹(x)9

Agregar una constante a la solución

=tan⁷(x)7 +tan⁹(x)9 +C

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

inversa -5x+e^x

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