计算下列不定积分(1)∫xe^(-3x)dx(2)∫xcos(4x+3)dx(3)∫xsin^2 xdx(4)∫x^2 lnxdx(5)求∫cos√xdx

Question

计算下列不定积分
(1)∫xe^(-3x)dx
(2)∫xcos(4x+3)dx
(3)∫xsin^2 xdx
(4)∫x^2 lnxdx
(5)求∫cos√xdx

Answer 1

1、-1/9*(1+3*x)*e^(-3*x)+C
2、1/16*cos(4*x+3)+1/16*(4*x+3)*sin(4*x+3)-3/16*sin(4*x+3)+C
3、x*(-1/2*cos(x)*sin(x)+1/2*x)+1/4*sin(x)^2-1/4*x^2+C
4、1/3*x^3*ln(x)-1/9*x^3+C
5、2*cos(x^(1/2))+2*x^(1/2)*sin(x^(1/2))+C