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How do you integrate #int e^(5x)(5)dx#?

Answer 1

Luke Alvarez

# int \ e^(5x)(5) \ dx = e^(5x) + c #

We can rewrite the integrand to get:

# int \ e^(5x)(5) \ dx = 5 \ int e^(5x) \ dx # # " " = (5 e^(5x))/5 + c # # " " = e^(5x) + c #

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Answer 2

Paisley Johnson

To integrate (\int e^{5x}(5)dx), you can use the substitution method. Let (u = 5x), then (du = 5dx).

The integral becomes (\frac{1}{5} \int e^u du).

Now, integrate (\int e^u du) which equals (e^u + C), where (C) is the constant of integration.

Substitute (u = 5x) back in: (\frac{1}{5}e^{5x} + 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.