Advertisements
Advertisements
Question
Integrate the following with respect to x.
log x
Solution
`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` |
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`sqrt(3x + 5)`
Integrate the following with respect to x.
If f'(x) = x + b, f(1) = 5 and f(2) = 13, then find f(x)
Integrate the following with respect to x.
`(x^3 + 3x^2 - 7x + 11)/(x + 5)`
Integrate the following with respect to x.
`(3x + 2)/((x - 2)(x - 3))`
Integrate the following with respect to x.
`(4x^2 + 2x + 6)/((x + 1)^2(x - 3))`
Integrate the following with respect to x.
`("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x)`
Integrate the following with respect to x.
`1/(x^2(x^2 + 1))`
Integrate the following with respect to x.
`1/(2x^2 - 9)`
Choose the correct alternative:
`int 2^x "d"x` is
Evaluate the following integral:
`int_0^1 sqrt(x(x - 1)) "d"x`
