Question

高数无穷积分

高数无穷积分仅第二小题，求助，无穷积分，
定积分不会计算

Answer 1

I = ∫e^(-ax)cosbxdx = (-1/a)∫cosbxde^(-ax)
= (-1/a)e^(-ax)cosbx - (b/a)∫e^(-ax)sinbxdx
= (-1/a)e^(-ax)cosbx + (b/a^2)∫sinbxde^(-ax)
= (-1/a)e^(-ax)cosbx + (b/a^2)e^(-ax)sinbx - (b^2/a^2)∫e^(-ax)cosbxdx
(a^2)I = -ae^(-ax)cosbx + be^(-ax)sinbx - (b^2)I
I = e^(-ax)(bsinbx-acosbx)/(a^2+b^2)
代入上下限，[e^(-ax)(bsinbx-acosbx)/(a^2+b^2)]<0, +∞>
= (0+a)/(a^2+b^2) = a/(a^2+b^2)

Answer 2

使用分部积分法
=-1/a*cosbxd(e^-ax)