不定积分最全公式_精品文档Word格式.docx
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6)∫sinxdx=-cosx+c
7)∫cosxdx=sinx+c
8)∫1/(cosx)^2dx=tanx+c
9)∫1/(sinx)^2dx=-cotx+c
10)∫1/√(1-x^2) dx=arcsinx+c
11)∫1/(1+x^2)dx=arctanx+c
12)∫1/(a^2-x^2)dx=(1/2a)ln|(a+x)/(a-x)|+c
13)∫secxdx=ln|secx+tanx|+c
14)∫1/(a^2+x^2)dx=1/a*arctan(x/a)+c
15)∫1/√(a^2-x^2) dx=arcsin(x/a)+c
16)∫sec^2xdx=tanx+c;
17)∫shxdx=chx+c;
18)∫chxdx=shx+c;
19)∫thxdx=ln(chx)+c;
1.∫adx=ax+C(a为常数)
2.∫sin(x)dx=-cos(x)+C
3.∫cos(x)dx=sin(x)+C
4.∫tan(x)dx=-loge|cos(x)|+C=loge|sec(x)|+C
5.∫cot(x)dx=loge|sin(x)|+C
6.∫sec(x)dx=loge|sec(x)+tan(x)|+C
7.∫sin2(x)dx
=
1
(x-sin(x)cos(x))+C
2
8.
x-
sin(2x)+C
4
9.∫cos2(x)dx
(x+sin(x)cos(x))+C
10.
x+
11.∫tan2(x)dx=tan(x)-x+C
12.∫cot2(x)dx=-cot(x)-x+C
13.∫sin(ax)sin(bx)dx
sin((a-b)x)
-
sin((a+b)x)
+C
2(a-b)
2(a+b)
14.∫sin(ax)cos(bx)dx
=-
cos((a-b)x)
cos((a+b)x)
15.∫cos(ax)cos(bx)dx
+
16.∫xsin(x)dx=sin(x)-xcos(x)+C
17.∫xcos(x)dx=cos(x)+xsin(x)+C
18.∫x2sin(x)dx=(2-x2)cos(x)+2xsin(x)+C
19.∫x2cos(x)dx=(x2-2)sin(x)+2xcos(x)+C
20.∫exdx=ex+C
21.
∫
a
dx=alog|x|
(a为常数)
x