# 不定積分の公式

1. ∫adx = ax+C (a は定数)
2. ∫x^adx = x^(a+1)/(a+1)+C (a != -1)
3. ∫x^(-1)dx = log(|x|)+C
4. ∫1/sqr(1-x^2)dx = arcsin(x)+C
5. ∫-1/sqr(1-x^2)dx = arccos(x)+C
6. ∫1/(1+x^2)dx = arctan(x)+C
7. ∫exp(x)dx = exp(x)+C
8. ∫a^xdx = a^x/log(a)+C
9. ∫log(x)dx = x(log(x)-1)+C
10. ∫sin(x)dx = -cos(x)+C
11. ∫cos(x)dx = sin(x)+C
12. ∫tan(x)dx = -loge|cos(x)|+C = loge|sec(x)|+C
13. ∫cot(x)dx = loge|sin(x)|+C
14. ∫sec(x)dx = loge|sec(x)+tan(x)|+C
15. ∫sin2(x)dx
 = 1 (x-sin(x)cos(x))+C 2
 = 1 x - 1 sin(2x)+C 2 4
16. ∫cos2(x)dx
 = 1 (x+sin(x)cos(x))+C 2
 = 1 x + 1 sin(2x)+C 2 4
17. ∫tan2(x)dx = tan(x)-x+C
18. ∫cot2(x)dx = -cot(x)-x+C
19. ∫sin(ax)sin(bx)dx
 = sin((a-b)x) - sin((a+b)x) +C 2(a-b) 2(a+b)
20. ∫sin(ax)cos(bx)dx
 = - cos((a-b)x) - cos((a+b)x) +C 2(a-b) 2(a+b)
21. ∫cos(ax)cos(bx)dx
 = sin((a-b)x) + sin((a+b)x) +C 2(a-b) 2(a+b)
22. ∫xsin(x)dx = sin(x)-xcos(x)+C
23. ∫xcos(x)dx = cos(x)+xsin(x)+C
24. ∫x2sin(x)dx = (2-x2)cos(x)+2xsin(x)+C
25. ∫x2cos(x)dx = (x2-2)sin(x)+2xcos(x)+C
26. ∫(1/cos2(x))dx = ∫(sec2(x))dx = tan(x)+C
27. ∫arcsin(x)dx = 1/2 log((1-cos(x))/(1+cos(x))) + C
= log(|tan(x/2)|) + C
28. ∫arccos(x)dx = 1/2 log((1+sin(x))/(1-sin(x))) + C
= log(|(1+tan(x/2))/(1-tan(x/2))|) + C
29. ∫arctan(x)dx = log(|sin(x)|) + C