x5+1 | x5−2x4+x3+2x4−4x3+2x2+3x3−6x2+3x+4x2−3x+1 | ||
= | = | ||
x3−2x2+x | x3−2x2+x |
4x2−3x+1 | ||
=x2+2x+3+ | ||
x3−2x2+x |
4x2−3x+1 | A | B | C | ||||
= | + | + | |||||
x3−2x2+x | x | x−1 | (x−1)2 |
4x2−3x+1 | 1 | 3 | 2 | ||||
= | + | + | |||||
x3−2x2+x | x | x−1 | (x−1)2 |
x5+1 | 1 | 3 | 2 | |||||
∫ | dx=∫(x2+2x+3+ | + | + | )dx = | ||||
x3−2x2+x | x | x−1 | (x−1)2 |
1 | 2 | |||
= | x3+x2+3x+ln|x|+3ln|x−1|− | +c | ||
3 | x−1 |
x | A | Bx+C | |||
= | + | ||||
1+x3 | 1+x | x2−x+1 |
x | 1 | 1 | 1 | x+1 | |||
=− | + | ||||||
1+x3 | 3 | 1+x | 3 | x2−x+1 |
1 | 1 | 1 | 2x−1 | 1 | 1 | ||||
∫(− | + | + | )dx = | ||||||
3 | 1+x | 6 | x2−x+1 | 2 | (x−1/2)2+3/4 |
1 | 1 | √3 | 2x−1 | |||||
= − | ln|1+x|+ | ln|x2−x+1|+ | arctg( | )+c | ||||
3 | 6 | 3 | √3 |
5^2 | 52 |
2^{10} | 210 |
a_2 | a2 |
a_{25} | a25 |
p{2} | √2 |
p{81} | √81 |
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