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Headinthesand (a) Integral from pi/6 to pi/4 of tan(x)e^(sec(x))sec(x)dx
use the substitution ... u = sec(x)
(b) integral from x=0 to ln(2) of (e^2x)/(1+e^x)dx
use the substitution ... u = 1+e^x
(c) antiderivative of 1/(a+b sqrt(x))dx
I'd try the substitution u = sqrt(x)
(d) antiderivative of (ln(x))^2 x
try the substitution u = ln(x) ... x = e^u
looks like integration by parts after that