1.求不定积分∫（x^2）dx/（x-1）,∫xsin（x^2+1）dx 2.已知∫f（x）dx=xe^x+才,则f（x）=
问题描述：
1.求不定积分∫（x^2）dx/（x-1）,∫xsin（x^2+1）dx 2.已知∫f（x）dx=xe^x+才,则f（x）=
答
∫（x^2）dx/（x-1）=∫(（x^2）-1+1)dx/（x-1）∫(x+1+1/（x-1）)dx =1/2*x^2 +x +ln(x-1)+C∫xsin（x^2+1）dx =1/2∫sin（x^2+1）d（x^2+1）=-1/2cos(x^2+1)∫f（x）dx=xe^xf(x) =(xe^x)'=(x+1)e^x...