Final Answer
Step-by-step Solution
Specify the solving method
Find the integral
Learn how to solve problems step by step online.
$\int\sqrt{\frac{x}{x-8}}dx$
Learn how to solve problems step by step online. Find the integral of w=(x/(x-8))^1/2. Find the integral. The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. We can solve the integral \int\frac{\sqrt{x}}{\sqrt{x-8}}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that \sqrt{x-8} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.