How do you integrate #int e^(x)/sqrt(e^(2x) +36)dx# using trigonometric substitution?
This simplifies nicely to
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To integrate ( \int \frac{e^x}{\sqrt{e^{2x} + 36}} , dx ) using trigonometric substitution, let ( e^x = 6 \tan \theta ). Then, ( dx = 6 \sec^2 \theta , d\theta ). Substitute these expressions into the integral. Simplify the integrand in terms of ( \theta ), perform the integration, and then convert back to the original variable ( x ). The final result is ( \frac{3}{\sqrt{3e^{2x} + 36}} + 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.
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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