How do I evaluate #inte^(2x)cosx dx# by parts?
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To evaluate the integral ∫e^(2x)cos(x) dx by parts:

Choose u and dv such that:
 u is differentiable and can be easily integrated.
 dv can be differentiated easily.

Calculate du and v:
 du is the derivative of u with respect to x.
 v is the integral of dv with respect to x.

Apply the integration by parts formula: ∫u dv = uv  ∫v du

Substitute the values of u, dv, du, and v into the integration by parts formula.

Evaluate the resulting integral and simplify if possible.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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