(17)∫(3
1+x
32 2 x2dx; 解 ∫(1+x2
x 2 x2dx=3∫11+x2dx 2∫1 x2dx=3arctanx 2arcsinx+C. (18)∫e(1 e x
xdx;
1
21 2x2 解 ∫e(1 xe x
xdx=∫(e xx )dx=ex+C.
(19)∫3xexdx;
(3e)x3xex
+C=+C. 解 ∫3edx=∫(3e)dx=ln(3e)ln3+1xxx
2 3x 5 2x
(20)∫dx; 3x
2(x
2 3 5 22x52x3+C=2x 解 ∫[25(]25dx= dx=x (+C. ∫23ln2 ln333xln3xx
(21)∫secx(secx tanx)dx;
解 ∫secx(secx tanx)dx=∫(sec2x secxtanx)dx=tanx secx+C.
x (22)∫cos2dx; 2
解 ∫cos2
(23)∫
解
x1+cosx11dx=∫dx=∫(1+cosx)dx=(x+sinx)+C. 22221dx; 1+cos2x111dx=dx=tanx+C. ∫1+cos2x∫2cos2x2