integral of e^xcos(x)

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∫ e^xcos(x)dx

Solution

e^xsin(x)2 +e^xcos(x)2 +C

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∫ e^xcos(x)dx

Apply Integration By Parts: e^xsin(x)−∫ e^xsin(x)dx

=e^xsin(x)−∫ e^xsin(x)dx

Apply Integration By Parts: −e^xcos(x)−∫ −e^xcos(x)dx

=e^xsin(x)−(−e^xcos(x)−∫ −e^xcos(x)dx)

Take the constant out: ∫a·f(x)dx=a·∫f(x)dx

=e^xsin(x)−(−e^xcos(x)−(−∫ e^xcos(x)dx))

Therefore

∫ e^xcos(x)dx=e^xsin(x)−(−e^xcos(x)−(−∫ e^xcos(x)dx))

Isolate ∫ e^xcos(x)dx

=e^xsin(x)2 +e^xcos(x)2

Add a constant to the solution

=e^xsin(x)2 +e^xcos(x)2 +C

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

integral of e^xcos(x)

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