Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`"e"^(2x)/("e"^(2x) - 2)`
Advertisements
उत्तर
Let f(x) = e2x – 2
Then f'(x) = 2e2x
So `int "e"^(2x)/("e"^(2x) - 2) "d"x = 1/2 int (2"e"^(2x))/("e"^(2x) - 2) "d"x`
= `1/2 int ("f'"(x))/("f"(x)) "d"x`
= `1/2 log|"f"(x)| + "c"`
= `1/2 log|"e"^(2x) - 2| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
`(8x + 13)/sqrt(4x + 7)`
Integrate the following with respect to x.
`(x^3 + 3x^2 - 7x + 11)/(x + 5)`
Integrate the following with respect to x.
xe–x
Integrate the following with respect to x.
`("e"^(3logx))/(x^4 + 1)`
Integrate the following with respect to x.
`1/(9 - 16x^2)`
Integrate the following with respect to x.
`sqrt(x^2 - 2)`
Integrate the following with respect to x.
`1/(x + sqrt(x^2 - 1)`
Choose the correct alternative:
`int "e"^x/sqrt(1 + "e"^x) "d"x` is
Evaluate the following integral:
`int 1/(sqrt(x + 2) - sqrt(x + 3)) "d"x`
Evaluate the following integral:
`sqrt(9x^2 + 12x + 3) "d"x`
