1 | ||
∫∞ | dx = // pomoże ktos? | |
(9x+9)7 |
dx | ||
A umiałbys policzyc ∫ | =∫x−7 dx? | |
x7 |
x−6 | ||
= | ||
6 |
1 | 9x+9−6 | 1 | ||||
∫0∞ | =∫9x+9−7= | =− | ||||
(9x+9)7 | 6 | 6 |
1 | 1 | |||
=− | * | |||
6 | 9x+9−6 |
1 | 1 | 1 | 1 | |||||
∫0∞ | =lim T−>∞ ∫0T | =lim T−>∞[− | * | ]0T=lim | ||||
9x+97 | 9x+9−7 | 6 | 9x+9−6 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||
T−>∞[− | * | + | * | ]=lim T−>[− | * | ]=− | czy | |||||||
3 | 9T+9−6 | 3 | 0 | 3 | 9T+9−6 | 3 |
1 | 1 | |||
zamiast − | oczywiscie mialo byc − | |||
3 | 6 |
1 | 1 | |||
∫ | dx= | +C | ||
(9x+9)7 | −54(9x+9)6 |
1 | ||
mi wychodzi, że całka ta jest równa | ||
54*96 |
1 | ||
∫ | dx= | |
(9x+9)7 |
1 | 9dx | |||
= | ∫ | = | ||
9 | (9x+9)7 |
1 | du | |||
= | ∫ | = | ||
9 | u7 |
1 | ||
= | ∫u−7du= | |
9 |
1 | u−6 | 1 | |||
= | = | = | |||
9 | −6 | −54u6 |
1 | ||
= | +C | |
−54(9x+9)6 |