Integration of sec^3[x]

L=Integral(sec^3(x) = Integral(sec^2(x)sec(x)dx now integrate by parts observing that sec^2(x) is the derivative of tan(x)

so, L=tan(x)sec(x)-Integral(tan^2(x)sec(x)dx… tan(x)sec(x)-Integral((sec^2(x)-1)sec(x)… dx=

tan(x)sec(x)-Integral(sec^3(x)dx+Integ…

NOTE : The bracket of ln(sec(x)+tan(x)) is not a bracket but an absolute value which I can't display here!

2L=tan(x)sec(x)+ln(abs.Value)(sec(x)+t…

L=(1/2)tan(x)sec(x)+(1/2)ln(abs.value)… which is the answer you require