# How do you integrate #int xcos(3x)# by integration by parts method?

We can rewrite:

The integral of the entire expression is therefore:

Hopefully this helps!

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To integrate ∫x*cos(3x) using integration by parts, you assign one part of the function as u and the other part as dv/dx. The formula for integration by parts is ∫u dv = uv - ∫v du.

Assign u = x and dv = cos(3x)dx. Then, differentiate u to find du/dx, and integrate dv to find v.

Next, apply the integration by parts formula, substituting the values of u, v, du/dx, and dv into the formula.

Finally, solve the resulting 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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