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Step-by-step Solution

Integrate x/((x^2-9)^0.5) from 3 to 5

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Answer

$4$

Step-by-step explanation

Problem to solve:

$\int_{3}^{5}\frac{x}{\sqrt{x^2-9}}dx$
1

Solve the integral $\int_{3}^{5}\frac{x}{\sqrt{x^2-9}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=x^2-9 \\ du=2xdx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{2x}=dx$

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Answer

$4$

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$\int_{3}^{5}\frac{x}{\sqrt{x^2-9}}dx$

Main topic:

Integration by substitution

Used formulas:

3. See formulas

Time to solve it:

~ 0.61 seconds