Question

Evaluate the integral [\int\frac{1}{(x^2\sqrt{x^2-16)}}dx\] using the substitution [x=4\sec\theta\].

Answer 1

using rigorous techniques of integral calculrs to integrate the given function above, the infinite integral equivalent is square root of (x2 - 16) - 4 arc tan ( square root of (x2 - 16) /4) + C where c is the constant. substituting x equals 4 sec theta, the equivalent is square root of (16/cos^2 theta - 16) - 4 arc tan ( square root of (16/cos^2 theta - 16) /4) + C.