What is the integral of #e^(2x)#?

Answer 1

The answer

#inte^(2x)*dx=1/2[e^(2x)]+c#

show below

#inte^(2x)*dx=1/2int2*e^(2x)*dx=1/2[e^(2x)]+c#
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Answer 2

#1/2e^(2x)+C#

Given: #inte^(2x) \ dx#.

We can manipulate as follows:

#inte^(2x) \ dx#
#=int1/2*2e^(2x) \ dx#
#=1/2int2e^(2x) \ dx#
Now, let #u=2x,:.du=2 \ dx,dx=(du)/2#
#=1/2int2e^u*(du)/2#
#=1/2inte^u \ du#
#=1/2e^u+C#
Replace back #u=2x# to get the final integral:
#=1/2e^(2x)+C#
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Answer 3

The integral of e^(2x) with respect to x is (1/2)e^(2x) + C, where C is the constant of integration.

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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.

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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