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Indefinite Integral – A quotient of functions with roots – Exercise 6605

Exercise

Evaluate the integral

\int \frac{x-7}{\sqrt{x+3}+\sqrt{x+5}} dx

Final Answer


\int \frac{x-7}{\sqrt{x+3}+\sqrt{x+5}} dx=

=-\frac{1}{5}{(x+3)}^{\frac{5}{2}}+\frac{10}{3}{(x+3)}^{\frac{3}{2}}+\frac{1}{5}{(x+5)}^{\frac{5}{2}}-4{(x+5)}^{\frac{3}{2}}+c

Solution

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