Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`(x^("e" - 1) + "e"^(x - 1))/(x^"e" + "e"^x)`
Advertisements
उत्तर
`(x^("e" - 1) + "e"^(x - 1))/(x^"e" + "e"^x) = (x^("" 1) + "e"^x/"e")/(x^"e" + "e"^x)`
= `("e"x^("e" - 1) + "e"^x)/("e"(x^"e" + "e"^x))`
Let f(x) = xe + ex
Then f'(x) = `"e"x^("e" - 1) + "e"^x`
So `int (x^("e" - 1) + "e"^(x - 1))/(x^"e" + "e"^x) "d"x = int ("e"x^("e" - 1) + "e"^x)/("e"(x^"e" + "e"^x)) "d"x`
= `1/"e" int ("f'"(x))/("f"(x)) "d"x`
= `1/"e" log |"f"(x)| + "c"`
= `1/"e" log|x^"e" + "e"^x| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`
Integrate the following with respect to x.
`[1 - 1/2]"e"^((x + 1/x))`
Integrate the following with respect to x.
`sqrt(1 - sin 2x)`
Integrate the following with respect to x.
`"e"^(3x) [(3x - 1)/(9x^2)]`
Integrate the following with respect to x.
`1/sqrt(x^2 + 6x + 13)`
Choose the correct alternative:
`int "e"^x/sqrt(1 + "e"^x) "d"x` is
Choose the correct alternative:
`int[9/(x - 3) - 1/(x + 1)] "d"x` is
Choose the correct alternative:
`int ("d"x)/sqrt(x^2 - 36) + "c"`
Evaluate the following integral:
`int ("d"x)/("e"^x + 6 + 5"e"^-x)`
Evaluate the following integral:
`sqrt(9x^2 + 12x + 3) "d"x`
