- #1
GreenPrint
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Evaluate
integral sqrt(9-x^2)/x dx
I get to here
-3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c
I plugged in for theta because originally I had this
-3 ln|csc(theta)+cot(theta)|+3cos(theta)+c
and I set x equal to a expression
x=3sin(theta)
Hence i had to change my equation back to terms of x because the original integral was in terms of so by solving for theta
theta=sin^-1(x/3)
-3 ln|csc(theta)+cot(theta)|+3cos(theta)+c = -3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c
but I'm lost as to why
-3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c=-3ln((sqrt(9-x^2)+3)/x)+sqrt(9-x^2)+c
and was hoping someone could explain why
integral sqrt(9-x^2)/x dx
I get to here
-3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c
I plugged in for theta because originally I had this
-3 ln|csc(theta)+cot(theta)|+3cos(theta)+c
and I set x equal to a expression
x=3sin(theta)
Hence i had to change my equation back to terms of x because the original integral was in terms of so by solving for theta
theta=sin^-1(x/3)
-3 ln|csc(theta)+cot(theta)|+3cos(theta)+c = -3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c
but I'm lost as to why
-3 ln|csc(sin^-1(x/2)+cot(sin^-1(x/3))|+3cos(sin^-1(x/3)+c=-3ln((sqrt(9-x^2)+3)/x)+sqrt(9-x^2)+c
and was hoping someone could explain why