Question

不定积分求解答

Answer 1

如图

Answer 2

1、原式=e^x+3sinx+5x+C
2、原式=∫[(x^4-1)/(1+x^2)+1/(1+x^2)]dx
=∫[x^2-1+1/(1+x^2)]dx
=(1/3)*x^3-x+arctanx+C
3、原式=(1/5)*∫(5x+7)^10 d(5x+7)
=(1/5)*(1/11)*(5x+7)^11+C
=(1/55)*(5x+7)^11+C
4、原式=ln|x-2|+C
5、原式=∫(lnx)^2 d(lnx)
=(1/3)*(lnx)^3+C
6、令t=√(x-1)，则x=t^2+1，dx=2tdt
原式=∫(t^2+1)t*2tdt
=2∫(t^4+t^2)dt
=(2/5)*t^5+(2/3)*t^3+C
=(2/5)*(x-1)^(5/2)+(2/3)*(x-1)^(3/2)+C
7、原式=∫xd(e^x)
=xe^x-∫e^xdx
=xe^x-e^x+C