Advertisements
Advertisements
प्रश्न
Integrate the following with respect to x.
`sqrt(4x^2 - 5)`
उत्तर
`int sqrt(4x^2 - 5) "d"x = int sqrt((2x)^2 - (sqrt(5))^2) "d"x`
Let 2x = t
Then 2dx = dt
= `1/2 int sqrt("t"^2 - (sqrt(5))^2) "dt"`
= `1/2 ["t"/2 sqrt("t"^2 - 5) - 5/2 log|"t" + sqrt("t"^2 - 5)|] + "c"`
= `1/4 [2x sqrt(4x^2 - 5) - 5 log|2x +sqrt(4x^2 - 5)| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the following with respect to x.
(3 + x)(2 – 5x)
Integrate the following with respect to x.
`(x^4 - x^2 + 2)/(x - 1)`
Integrate the following with respect to x.
`(3x^2 - 2x + 5)/((x - 1)(x^2 + 5))`
Integrate the following with respect to x.
`"e"^(xlog"a") + "e"^("a"log"a") - "e"^("n"logx)`
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.
`x^5 "e"^x`
Choose the correct alternative:
`int 2^x "d"x` is
Choose the correct alternative:
`int "e"^x/sqrt(1 + "e"^x) "d"x` is
Choose the correct alternative:
`int_2^4 ("d"x)/x` is
Evaluate the following integral:
`sqrt(9x^2 + 12x + 3) "d"x`
