Indefinite integral of √(49-x^2)/(x^2)?
Just wondering if anyone can help me with this problem. It is the indefinite integral of √(49-x^2) divided by (x^2). Only the 49-x^2 is rooted. Can anyone help? Thanks.
Update:Where did you get the formula to get the x^2 on the bottom to just be x?
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∫(√(49 - x²)/x² )dx = - √(49 - x²)/x - ∫(-1/x)(- x/√(49 - x²) dx =
= - √(49 - x²)/x - ∫dx/√(49 - x²) = - √(49 - x²)/x - arcsin (x/7) + C
x = 7u
u = x/7
dx = 7 du
∫dx/√(49 - x²) = ∫7 du/√(49 - 49u²) = ∫7 du/(7√(1 - u²)) = ∫du/√(1 - u²) =
= arcsin u + C = arcsin (x/7) + C