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JH
Numerade Educator

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Problem 74 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{4^x + 10^x}{2^x}\ dx $

Answer

$\frac{2^{x}}{\ln 2}+\frac{5^{x}}{\ln 5}+C$

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Video Transcript

for this in a girl. Let's just go ahead and briefest into two fractions. So we have four x over to the ex. Tend to the X over two to the ex. And then here we can use the fact that eighteen eggs over beat in X is a over B to the X that she's using laws of experiments. So here will just have four or three to the ex ten over to to the ex. Now let's simplify these. That's just two decks and then fact to the ex, and we could have a formula for these exponential inaugurals. This is just eight of the X over the natural log of a plus he and here is a verification of this. If you forgot this fact, you could just check that. This is true, because if you differentiate this over here, you will get eight X over Helen A. But then you also have to multiply by Ellen A. When you differentiate the index so those would cancel. The Z will go to zero and you will be left over with the inside grand. So here, using that formula twice once for the two and then once for the five, let's add that constant of integration, see, And that's your final answer