(nie, nie jest to oczywiste jak ci się może "wydawać")
∫(a+x1/3)5dx
x=t3
dx=3t2dt
| 1 | ||
3∫(a+t)5t2dt = | (a+t)6t2−∫(a+t)6tdt = | |
| 2 |
| 1 | 1 | 1 | ||||
(a+t)6t2− | (a+t)7t+ | ∫(a+t)7dt= | ||||
| 2 | 7 | 7 |
| 1 | 1 | 1 | ||||
= | (a+t)6t2− | (a+t)7t+ | (a+t)8 = | |||
| 2 | 7 | 56 |
| 1 | 1 | 1 | ||||
= | (a+3√x)63√x2− | (a+3√x)73√x+ | (a+3√x)8+c | |||
| 2 | 7 | 56 |