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How do you evaluate the integral #int3e^(x)-5e^(2x) dx#?

Answer 1

Emma Aldridge

#int 3e^x-5e^{2x}dx=3e^x-5/2e^{2x}+C#

Let us look at some details.

Remember:

#int e^x dx=e^x+C#

#int e^{kx} dx=e^{kx}/k+C#

Now, let us work on the integral.

#int 3e^x-5e^{2x}dx#

by applying integral on each term,

#=int 3e^x dx -int 5e^{2x}dx#

by pulling constants out of the integrals

#=3int e^x dx-5int e^{2x}dx#

by applying the formulas above,

#=3e^x-5e^{2x}/2+C#

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Answer 2

Isabella Ackerman

To evaluate the integral ( \int 3e^x - 5e^{2x} , dx ), integrate each term separately using the power rule for exponential functions. The antiderivative of ( e^x ) is ( e^x ), and the antiderivative of ( e^{2x} ) is ( \frac{1}{2}e^{2x} ). Then, apply the integration constant as needed.

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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.