integrate from 0 to pi/4 (sec^2x)/((1+7tanx)^2)^1/3

Question

integrate form pi^2/36 to pi^2/4 (cos(x^1/2))/(xsin(x^1/2))^1/2

integrate from 0 to pi/3 (tanx)/(2secx)^1/2

Answer 1

if we let
u = 1+7tanx
du = 7sec^2 x dx
and you have ∫ u^(-1/3) 1/7 du

if we let
u = sin√x
du = cos√x * 1/(2√x)
and you have ∫ 1/√u 2 du