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The_ArtofScience
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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
The_ArtofScience said:Integrate (a^x + b^x)^3 /((a^x)*(b^x))
The_ArtofScience said:But then what do I do with this strange exponent? I don't know how to integrate an expression like b^x
The formula for integrating (a^x + b^x)^3 /((a^x)*(b^x)) is ∫(a^x + b^x)^3 /((a^x)*(b^x)) dx.
The process for integrating (a^x + b^x)^3 /((a^x)*(b^x)) involves using the substitution method or the logarithmic differentiation method.
When choosing a substitution for integrating (a^x + b^x)^3 /((a^x)*(b^x)), it is important to choose a variable that will simplify the integrand and make it easier to integrate. Common choices include u = a^x or u = b^x.
Yes, the logarithmic differentiation method can be used to integrate (a^x + b^x)^3 /((a^x)*(b^x)). This method involves taking the natural logarithm of both sides of the equation and using the product and chain rules to simplify the integrand.
Some common mistakes to avoid when integrating (a^x + b^x)^3 /((a^x)*(b^x)) include forgetting to apply the chain rule, not simplifying the integrand before integrating, and making a mistake in the substitution chosen.