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प्रश्न
Integrate the following with respect to x.
log x
उत्तर
`int log x "d"x = int"udv"`
`int "udv" = "uv" - int "vdu"`
`int log x "d"x = (log x) (x) - int (x) (("d"x)/x) + "c"`
= `x log x - int "d"x + "c"`
= x log x – x + c
= x(log x – 1) + c
| Successive derivatives | Repeated Integrals |
|
Taken u = log x uI = `1/x` `"du"/("d"x) = 1/x` du = `("d"x)/x` |
dv = dx `int "d"x = int "d"x` |
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