- #1

- 83

- 0

## 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

- Thread starter The_ArtofScience
- Start date

- #1

- 83

- 0

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

Science Advisor

Homework Helper

- 25,832

- 251

(try using the X

erm … just expand it …Integrate (a^x + b^x)^3 /((a^x)*(b^x))

(a

- #3

- 83

- 0

(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

Science Advisor

Gold Member

- 1,779

- 20

[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

Science Advisor

Homework Helper

- 25,832

- 251

(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

Science Advisor

Gold Member

- 1,779

- 20

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

- #7

- 83

- 0