求解数学题∫(3t+1)/(t*t-t+1)
网友回答
∫(3t+1)/(t²-t+1)dt
=∫[3(t-1/2)+5/2]/[(t-1/2)²+3/4]dt
=3∫(t-1/2)/[(t-1/2)²+3/4]d(t-1/2)+5{∫1/[(t-1/2)²+3/4]d(t-1/2)}/2
=3{∫1/[(t-1/2)²+3/4]d[(t-1/2)²+3/4]}/2+5{∫1/[(t-1/2)²+(√3/2)²]d(t-1/2)}/2
=3ln(t²-t+1)/2+2√3arctan(2√3x/3)/3+C
======以下答案可供参考======
供参考答案1:
分离啊 把它分成 ∫1/（t+b）^2dt+∫1/(t+c)dt 再用公式 即可 大哥啊这可是最基本的啊