# How do you integrate #int e^(3x)cos(2x)# by integration by parts method?

I got:

BUT check my maths.

So basically we get:

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To integrate ( \int e^{3x}\cos(2x) ) using the integration by parts method, you would assign one function as ( u ) and the other as ( dv ). Let ( u = e^{3x} ) and ( dv = \cos(2x)dx ). Then, you would differentiate ( u ) and integrate ( dv ) to find ( du ) and ( v ), respectively. After that, you would apply the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

Substitute the values of ( u ), ( v ), ( du ), and ( dv ) into the formula, then evaluate the integral.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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