`int 6/sqrt(10x-x^2) dx` Find the indefinite integral

Expert Answers

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Take the constant out ,


Let's rewrite the denominator by completing the square,


Now apply integral substitution: `u=x-5`




Again apply integral substitution: `u=5sin(v)`




Use the trigonometric identity: `cos^2(x)=1-sin^2(x)`


`=6int(5cos(v))/(5cos(v))dv` , assuming `cos(v)>=0`



substitute back `v=arcsin(u/5)` and `u=(x-5)`  


Add a constant C to the solution,



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