1) ∫dx/sqrt(2x + 3) = 1/2∫d(2x+3)/sqrt(2x+3) = sqrt(2x+3) + C
3) ∫(0;π/6)e^(sinx)cosxdx = ∫(0;π/6)e^(sinx)dsinx = e^(sinx)|(0;π/6) = sqrt(e) - 1
5)∫(1;8)log(8,x)dx = 1/ln8(xlnx - x)|(1;8) = 8 - 9/ln8
2) ∫cos(sqrt(x))/sqrt(x)dx = 2∫cos(sqrt(x))dsqrt(x) = 2sin(sqrt(x))
4) ∫xdx/sin^2(x) = -∫xdctgx = -xctgx + ∫ctgxdx = -xctgx + ∫dsinx/sinx = -xctgx + ln(sinx) + C