Advertisements
Advertisements
Question
Integrate the following with respect to x.
`("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x)`
Solution
`int ("a"^x - "e"^(xlog"b"))/("e"^(x log "a") "b"^x) "d"x = int ("a"^x - "e"^(log("b")^x))/("e"^(log"a"^x) ("b")^x) "d"x`
= `int ("a"^x - "b"^x)/("a"^x"b"^x) "d"x`
= `int ("a"^x/("a"^x"b"^x) - "b"^x/("a"^x"b"^x)) "d"x`
= `int (1/"b"^x - 1/"a"^x) "d"x`
= `int ("b"^-x - "a"^-x) "d"x`
= `"b"^-x/((-1) log |"b"|) - "a"^-x/((-1) log|"a"|) + "c"`
= `"a"^-x/(log|"a"|) - "b"^-x/(log|"b"|) + "c"`
= `1/("a"^x log|"a"|) - 1/("b"^x log|"b"|)+ "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`(9x^2 - 4/x^2)^2`
Integrate the following with respect to x.
`(3x + 2)/((x - 2)(x - 3))`
Integrate the following with respect to x.
If f'(x) = ex and f(0) = 2, then find f(x)
Integrate the following with respect to x.
`sqrt(1 - sin 2x)`
Integrate the following with respect to x.
x3e3x
Integrate the following with respect to x.
`(log x)^3/x`
Integrate the following with respect to x.
x8(1 + x9)5
Integrate the following with respect to x
`1/(x log x)`
Integrate the following with respect to x.
`1/(x + sqrt(x^2 - 1)`
Choose the correct alternative:
`int_0^(pi/3) tan x "d"x` is
