# How do you evaluate the integral #int cos(root3x)#?

Now we perform integration by parts. Let:

Then:

Integration by parts again:

Paying attention to sign:

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To evaluate the integral ∫ cos(√3x) dx, you can use a substitution method. Let u = √3x, then du = √3 dx. Solving for dx, you get dx = du/√3. Substitute these into the integral:

∫ cos(√3x) dx = ∫ cos(u) * (du/√3) = (1/√3) ∫ cos(u) du

Now, integrate cos(u) with respect to u:

(1/√3) ∫ cos(u) du = (1/√3) * sin(u) + C

Substitute back u = √3x:

(1/√3) * sin(√3x) + C

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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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