# How do you evaluate the integral #int xsec(4x^2+7)#?

Hence,

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The answer is

We need

We perform this integral by substitution

Let

Therefore,

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To evaluate the integral ∫xsec(4x^2+7), we can use u-substitution. Let u = 4x^2 + 7. Then du/dx = 8x, which implies dx = du/(8x).

Substituting u and dx into the integral, we get:

∫xsec(u) * (1/(8x)) du

Simplify to get:

(1/8) * ∫sec(u) du

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

(1/8) * ln|sec(u) + tan(u)| + C

Finally, substitute back u = 4x^2 + 7:

(1/8) * ln|sec(4x^2 + 7) + tan(4x^2 + 7)| + 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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