How do you integrate #int 6^x2^xdx# from #[1,e]#?
The answer is
Therefore
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To integrate ( \int_{1}^{e} (6^x  2^x) , dx ):

Integrate ( 6^x ): [ \int 6^x , dx = \frac{6^x}{\ln(6)} ]

Integrate ( 2^x ): [ \int 2^x , dx = \frac{2^x}{\ln(2)} ]
Now, compute each integral separately over the interval [1,e] and subtract the results:
[ \int_{1}^{e} 6^x , dx = \frac{6^e  6^1}{\ln(6)} ]
[ \int_{1}^{e} 2^x , dx = \frac{2^e  2^1}{\ln(2)} ]
Finally, subtract the second integral from the first:
[ \int_{1}^{e} (6^x  2^x) , dx = \frac{6^e  6^1}{\ln(6)}  \frac{2^e  2^1}{\ln(2)} ]
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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