求下列不定积分和定积分1.∫（3/X+2e的X次方-1/X乘根号下X）dx2.∫上面是2,下面是1（根号下为X,根号外-1）dx3.∫上面是四分之派,下面是六分之派COS2Xdx

Question

求下列不定积分和定积分
1.∫（3/X+2e的X次方-1/X乘根号下X）dx
2.∫上面是2,下面是1（根号下为X,根号外-1）dx
3.∫上面是四分之派,下面是六分之派COS2Xdx

Answer 1

1.∫[(3/x)+2e^x-(1/x√x)]dx
=∫(3/x)dx+2∫(e^x)dx-∫[x^(-3/2)]dx
=3lnx+2e^x+2x^(-1/2)+C
=3lnx+2e^x+2/√x+C
2.∫(2,1)(√x-1)dx
=[(2/3)x^(3/2)-x]|(2,1)
=[(2/3)*2^(3/2)-2]-[(2/3)*1^(3/2)-1]
=(4√2-5)/3
3.∫(π/4,π/6)cos2xdx
=(1/2)∫(π/4,π/6)cos2xd2x
=(1/2)sin2x|(π/4,π/6)
=(1/2)(sinπ/2-sinπ/3)
=(2-√3)/4