不定积分要快啊,我要交了.求下列不定积分(凑微分法）:(1)∫x+1/(x^2+2x+3)^1/4dx(2)∫e^xcos(e^x)dx(3)∫1/2xdx(4)∫(x^3-x)(3x^2)dx(5)∫(根号x+1)^5/根号xdx(6)∫e根号x/根号xdx（7）∫x^

Question

不定积分 要快啊,我要交了.
求下列不定积分(凑微分法）:(1)∫x+1/(x^2+2x+3)^1/4dx (2)∫e^xcos(e^x)dx (3)∫1/2x dx (4)∫(x^3-x)(3x^2)dx (5)∫(根号x+1)^5/根号x dx (6) ∫e根号x/根号x dx （7）∫x^2ex^3+1 dx (8)∫xe^-2x^2
(9)e^x/根号1+2e^x (10)∫sin2/3x dx (11)∫1/x^2 sin1/x dx (12)∫1/x(ln根号x)^3 dx
(分部积分法）：（1）∫xe^3xdx (2)∫xsin1/2xdx (3)∫x^2cosxdx (4)∫xsin(x+1)dx (5) ∫xln(x-1)dx
（8）、（9）打字打少了dx

Answer 1

=∫x+1/(x^2+2x+3)^1/4dx =2∫(x^2+2x+3)^1/4d(x^2+2x+3)=2∫(x^2+2x+3)^1/4d(x^2+2x+3)=2/3(x^2+2x+3)^3/4+C

=∫cos(e^x)de^x=sine^x+c

=1/2∫x dx =1/4x^2+c

=^3∫(x^3-x)(x^2)dx =^3∫(x^3-x)x^2dx=^3(∫x^5/6-x^3/2)dx=11乘以根号3乘以x^11/6/6-2乘以根号3乘以x^5/2/5+c

=-2∫(x+1)^5d(x+1)^2=-5/3(x+1)^6/5+c

=-2∫e^x2dx^2=-2e^x2+c

怀疑你抄错题了=-2∫ex^2dx^2+x=-2ex^2+x+c

=∫e^xdx-2∫x^2dx=e^x-4/3x^3/2+c

=  ∫de^x/(1+2e^x)^2=1/2∫d(2e^x+1)/(1+2e^x)^2=(1+2e^x)^2+c

=3/2∫sin2/3x d2/3x =-3/2cos2/3x+c

=-∫sin1/x d1/x =cos1/x+c

=∫dlnx/lnx^3=3∫dlnx/lnx=3lnlnx+c

=1/3∫xe^3xd3x =1/3∫xde^3x =1/3xe^3x-1/9∫e^3xd3x=1/3xe^3x-1/9e^3x+c临时有事,剩下的自己做吧