find the integral of 10/(sqrt(64-x^2))

Question

I need help finding the answer to the above question.  I thought the answer is arcsin(10x/8) but I can't put in "arcsin" in webassing (or I haven't found out how to do that)

Answer 1

∫10/(64 - x^2)^1/2 dx

let

I = 10∫1/(8^2 - x^2)^1/2dx

let ... x = 8sinq

q=arcsin(x/8)

dx/dq = 8cosq

dx = 8cosq dq

I = 10∫8cosq/(64 - 64cos^2q)^1/2 dq

I = 10∫8cosq/8cosq dq

I = 10q + c

∫10/(64 - x^2)^1/2 dx = 10arcsin(x/8) + c