Таблицы интергалы, производные, тригонометрические функции
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Таблица основных интегралов |
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1 |
xn dx |
xn+1/n+1 + C |
2 |
*x dx |
2x3/2/3+ C |
3 |
*1/x dx |
2x + C |
4 |
*1/x dx |
ln|x| + C |
5 |
ax dx |
ax / ln a + C |
6 |
ekx dx |
ekx/k + C |
7 |
sin ax dx |
-1/a cos ax + C |
8 |
cos ax dx |
1/a sin ax + C |
9 |
tg x dx |
-ln cosx + C |
10 |
ctg x dx |
ln sinx + C |
11 |
1/cos2ax dx |
1/a tg ax + C |
12 |
1/sin2ax dx |
-1/a ctg ax + C |
13 |
x/x2+a dx |
½ ln|x2+ a| + C |
14 |
x/x2+a2 dx |
1/a arctgx/a +C |
15 |
x/a2 -x2 dx |
arcsin x/a +C |
16 |
1/x2+a dx |
ln|x| + x2 +a + C |
17 |
1/x2-a dx |
ln|x-a/x+a| + C |
a |
0 |
p/6 |
p/4 |
p/3 |
p/2 |
2p/3 |
p |
3p/2 |
sin a |
0 |
1/2 |
√2/2 |
√3/2 |
1 |
√3/2 |
0 |
-1 |
cos a |
1 |
√3/2 |
√2/2 |
1/2 |
0 |
-1/2 |
-1 |
0 |
tg a |
0 |
1/√3 |
1 |
√3 |
-- |
-√3 |
0 |
-- |
ctg a |
-- |
Ö3 |
1 |
1/√3 |
0 |
-1/√3 |
-- |
0 |
Таблица производных |
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1 |
const |
0 |
2 |
xn |
nxn-1 |
3 |
Öx |
1/2Öx |
4 |
1/x |
-1/x2 |
5 |
sinx |
cosx |
6 |
cosx |
-sinx |
7 |
tgx |
1/sinx |
8 |
ctg x |
-1/ sinx |
9 |
arcsinx |
1/Ö1-x2 |
10 |
arccosx |
-1/Ö1-x2 |
11 |
arctgx |
1/Ö1 + x2 |
12 |
arcctg x |
-1/Ö1+x2 |
13 |
lnx |
1/x |
14 |
logax |
1/x lnx |
15 |
ex |
ex |