Advertisements
Advertisements
Question
Integrate the following with respect to x.
`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`
Solution
`("e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)) "d"x`
- `int ("e"^(log "a"^x) + "e"^(log "a"^"a") - "e"^("a" log x^"n")) "d"x`
= `int ("a"^1 + "a"^"a" - x^"n") "d"x`
= `["a"^x/(log|"a"|) + "a"^"a" (x) - (x^("n" + 1))/(("n" + 1))] + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`(4x^2 + 2x + 6)/((x + 1)^2(x - 3))`
Integrate the following with respect to x.
`("e"^(3x) - "e"^(-3x))/"e"^x`
Integrate the following with respect to x.
`[1 - 1/2]"e"^((x + 1/x))`
Integrate the following with respect to x.
sin3x
Integrate the following with respect to x.
`(log x)^3/x`
Integrate the following with respect to x.
`1/(x^2(x^2 + 1))`
Integrate the following with respect to x.
`1/(9 - 8x - x^2)`
Integrate the following with respect to x.
`1/sqrt(x^2 - 3x + 2)`
Choose the correct alternative:
`int_0^(pi/3) tan x "d"x` is
Evaluate the following integral:
`sqrt(9x^2 + 12x + 3) "d"x`
