Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Find the integral
- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- Homogeneous Differential Equation
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
- Integrate by substitution
- Integrate by parts
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Find the integral
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$\int\sqrt{\frac{x}{x-8}}dx$
Learn how to solve equations 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.