Question

求做数学题 积分计算 谢谢

求过程 谢谢

Answer 1

Answer 2

13.
=(1/3)e^(3x)x^2-(2/3)∫xe^(3x)dx
=(1/3)e^(3x)x^2-(2/9)e^(3x)x+(2/9)∫e^(3x)dx
=(1/3)e^(3x)x^2-(2/9)e^(3x)x+(2/27)e^(3x)+C
=(1/27)(9x^2-6x+2)e^(3x)|（-∞，0）

=2/27
14.=∫(cos(x/2))^2-(sin(x/2))^2/|sin(x/2)+cos(x/2)|dx

因为积分区间为(0,π/6) 所以,sin(x/2)+cos(x/2)>0
则原式=∫(cos(x/2)-(sin(x/2))（sin(x/2)+cos(x/2)）/(sin(x/2)+cos(x/2))dx
=∫(cos(x/2)-(sin(x/2))dx
=2sin(x/2)+2cosx(x/2)|(0,π/6)
=2[sin(π/12)+cos(π/12)-1]
15.
=∫[(x+7/2)-7/2]/√（2x+7)dx
=1/2∫√（2x+7)dx-7/2*1/√（2x+7)dx
=1/6（2x+7）^(3/2)-7/2(2x+7)^(1/2)+C