习题4 1
1. 求下列不定积分:
1 (1)∫2dx; x
111 解 ∫2dx=∫x 2dx=x 2+1+C= +C. 2+1xx
(2)∫xxdx;
解 ∫xxdx=∫
1
x3x2dx=13+123+12x2+C=5x2x+C. (3)∫
解 dx; ∫1
xdx=∫x 1
2dx= 11x2+C=2x+C. 1 +121
(4)∫x2xdx;
解 ∫x2xdx=∫7
x3dx=1
7+137+13x+C=33xx+C. 10
(5)∫
解 1x2x1dx; dx=∫x ∫x2x52dx= 1311x2+C= +C. 52xx +125
(6)∫xndx;
解 ∫xdx=∫nnxmdx=1
n+1mn+1xm+C=mxn+mm+nm+C.
(7)∫5x3dx;
5 解 ∫5x3dx=5∫x3dx=x4+C. 4
(8)∫(x2 3x+2)dx;
13 解 ∫(x2 3x+2)dx=∫x2dx 3∫xdx+2∫dx=x3 x2+2x+C. 32