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How do you evaluate the integral #int dx/e^(3x)#?

Answer 1

Paisley Johnson

#=-1/3e^(-3x)+c#

You can rewrite the expression as:

#-1/3int-3e^(-3x)dx#

Then you can get:

#=-1/3e^(-3x)+c#

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Answer 2

Paisley Johnson

To evaluate the integral ∫ dx/e^(3x), you can use the substitution method. Let u = 3x, then du = 3dx. Rearranging, dx = du/3. Substituting these into the integral, you get:

∫ dx/e^(3x) = ∫ (du/3) / e^u

This simplifies to:

(1/3) ∫ du/e^u

Integrating du/e^u gives:

(1/3) ∫ e^(-u) du = (1/3) * (-e^(-u)) + C

Substituting back u = 3x:

= -(1/3) * e^(-3x) + C

So, the integral evaluates to:

-(1/3) * e^(-3x) + C

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Answer from HIX Tutor

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.