Chapter6: Exponential And Logarithmic Functions
Section6.7: Exponential And Logarithmic Models
Problem 27SE: Prove that bx=exln(b) for positive b1 .
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Transcribed Image Text:Evaluate the indefinite integral.
dx
2 5x
Step 1
We must decide what to choose for u.
If u = f(x), then du = f '(x) dx, and so it is helpful to look for some expression in
dx
dx for which the derivative is also present, though perhaps missing a constant
2 - 5x
2 - 5x
factor.
We see that 2 – 5x is part of this integral, and the derivative of 2 - 5x is -5
-5
, which is simply
a constant.
Step 2
If we choose u = 2 - 5x, then du = -5 dx.
dx
2 - 5x
dx
If u = 2- 5x is substituted into
then we have
*xp
2 - 5x'
We must also convert dx into an expression involving u.
du.
Using du = -5 dx, then we get dx =
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