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How do you integrate #int 3^xdx#?

Answer 1

Charles Arocha

The answer is #=3^x/ln3+C#

Let #u=3^x#

Taking logs on both sides

#lnu=ln(3^x)=xln3#

Then

#u=e^(xln3)#

Therefore,

#int3^xdx=inte^(xln3)dx=e^(xln3)/(ln3)+C#

#=3^x/ln3+C#

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Answer 2

Charles Anctil

To integrate ( \int 3^x , dx ), you can use the power rule of integration. Since ( 3^x ) is an exponential function, its antiderivative involves the same function. The integral is:

[ \int 3^x , dx = \frac{1}{\ln(3)} \cdot 3^x + 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.