How do I evaluiate #intsec(x)(sec(x) + tan(x)) dx#?
I don't believe that there is any trigonometric substitution involved here actually.
Now, using the change of variable rule, we get:
And there you have it!
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To evaluate ( \int \sec(x)(\sec(x) + \tan(x)) , dx ), use the substitution method. Let ( u = \sec(x) + \tan(x) ). Then ( du = (\sec(x)\tan(x) + \sec^2(x)) , dx ), and ( \sec(x)\tan(x) = u - \sec^2(x) ).
Substitute ( u ) and ( du ) into the integral, which simplifies it to ( \int u , du ).
Integrating ( u ) with respect to ( u ) gives ( \frac{1}{2}u^2 + C ), where ( C ) is the constant of integration.
Finally, substitute back ( u = \sec(x) + \tan(x) ) to obtain the final result.
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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.
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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