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## Homework Statement

Integrate (a^x + b^x)^3 /((a^x)*(b^x))

## The Attempt at a Solution

I have only 2 semesters of calculus under my belt yet nothing in my experience has taught me to do anything like this

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- Thread starter The_ArtofScience
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- #1

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Integrate (a^x + b^x)^3 /((a^x)*(b^x))

I have only 2 semesters of calculus under my belt yet nothing in my experience has taught me to do anything like this

- #2

tiny-tim

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(try using the X

Integrate (a^x + b^x)^3 /((a^x)*(b^x))

erm … just expand it …

(a

- #3

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(a^3x + 3a^2x b^x + 3a^x b^2x + b^3x)/(a^x b^x)

= (a^2 /b)^x + 3a^x + 3b^x + (b^2/a)^x

But then what do I do with this strange exponent? I don't know how to integrate an expression like b^x

- #4

Born2bwire

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[tex]\log_b(b^x) = x[/tex]

[tex]\frac{d}{dx}\log_b(b^x) = 1[/tex]

[tex]\frac{d}{dx}\log_b(b^x) = \frac{d}{du} \log_b(u) \cdot \frac{d b^x}{dx}[/tex] where [tex]u = b^x[/tex].

Convert [tex]log_b(u) = \frac{\ln(u)}{\ln(b)}[/tex] and go from there.

- #5

tiny-tim

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But then what do I do with this strange exponent? I don't know how to integrate an expression like b^x

(

Yes, use

or write b

so (b

- #6

Born2bwire

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Oh sure, do it the easy and efficient way. ;)

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