Question

evaluate the integral of

dx/square root of 9-8x-x^2

Answer 1

9-8x-x^2 = 25 - (16 + 8x + x^2) = 3^2 - (x-4)^2

Integral sqrt(a^2 - u^2) du = u/2 * sqrt(a^2 - u^2) + a^2/2 arcsin(u/a)

just plug in a=5 and u=x-4 and plug away.

This is a standard trig substitution and integration by parts.

Answer 2

typo: 5^2 not 3^2

Answer 3

Go on: wolframalpha dot com

When page be open in rectangle type:

integrate dx/sqrt(9-8x-x^2)

and click option =

After few seconds when you see result click option: Show steps