Solution: Deriving formulas Evaluate the following

Chapter 7, Problem 74AE

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QUESTION:

Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is an integer.

\(\int \frac{x}{\sqrt{a x+b}} d x\); Use \(u^{2}\) = ax + b.

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QUESTION:

Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is an integer.

\(\int \frac{x}{\sqrt{a x+b}} d x\); Use \(u^{2}\) = ax + b.

ANSWER:

Problem 74AE

Deriving formulas Evaluate the following integrals. Assume a and b are real numbers and n is an integer. , use

Solution

Step 1

In this problem we have to evaluate  

Consider   … (1)

Take

Differentiating we get

     (since )

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