Final answer to the problem
$-5\ln\left|\frac{5+\sqrt{25-x^2}}{x}\right|+\sqrt{25-x^2}+C_0$
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Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(((25-x^2)^(1/2))/x)dx. We can solve the integral \int\frac{\sqrt{25-x^2}}{x}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Factor the polynomial 25-25\sin\left(\theta \right)^2 by it's greatest common factor (GCF): 25.
Final answer to the problem
$-5\ln\left|\frac{5+\sqrt{25-x^2}}{x}\right|+\sqrt{25-x^2}+C_0$
