Advertisements
Advertisements
Question
Integrate the following with respect to x.
`"e"^x [1/x^2 - 2/x^3]`
Advertisements
Solution
Letf(x) = `(-1)/x^2`
Then f'(x) = `(-2)/x^3`
So `int "e"^x [1/x^2 - 2/x^3] "d"x = int "e"^x ["f"(x) + "f'"(x)] "d"x`
= `"e"^x "f"(x) + "c"`
= `"e"^x/x^2 + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`(8x + 13)/sqrt(4x + 7)`
Integrate the following with respect to x.
`x^3/(x + 2)`
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(log x)^2`
Integrate the following with respect to x
`1/(x log x)`
Integrate the following with respect to x.
`"e"^(3x) [(3x - 1)/(9x^2)]`
Integrate the following with respect to x.
`sqrt(1 + x + x^2)`
Choose the correct alternative:
`int sqrt("e"^x) "d"x` is
Choose the correct alternative:
`int "e"^(2x) [2x^2 + 2x] "d"x`
Evaluate the following integral:
`int_0^3 (x dx)/(sqrt(x + 1)+ sqrt(5x + 1))`
