dt=2xdx⇒dx=dt2x Step 2: Substitute into the integralNow, substitute t and dx into the integral:∫xex2dx=∫xet⋅dt2x Step 3: Simplify the integralThe x in the numerator and denominator cancels out:∫xex2dx=∫12etdt Step 4: IntegrateNow, we can integrate:∫12etdt=12et+Cwhere C ...
(2)1. -解析 u s ∫_0^12^xe^xdx =∫_0^12^xde^x =2e—ed2分步积分法: ∫udv=uv-∫vdu =2^2e^x|_0^1-e^x_2^xln21^1 =2e(1-1n2)+1n2-1. 2s ∫_(-1)^1|x^2-x|dx x^2-x=x(x-1) 且xc[.1] 得X.0]时x ∈[-1, x^2-x≥0 x[0.1]时x x^2-x≤0 ∴...