Advertisements
Advertisements
Question
Integrate the following with respect to x.
`sqrt(4x^2 - 5)`
Advertisements
Solution
`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
RELATED QUESTIONS
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.
`("e"^(3x) +"e"^(5x))/("e"^x + "e"^-x)`
Integrate the following with respect to x.
2 cos x – 3 sin x + 4 sec2x – 5 cosec2x
Integrate the following with respect to x
`1/(x log x)`
Integrate the following with respect to x.
`1/(9 - 16x^2)`
Integrate the following with respect to x.
`1/(2x^2 - 9)`
Integrate the following with respect to x.
`x^3/sqrt(x^8 - 1)`
Choose the correct alternative:
`int_0^1 sqrt(x^4 (1 - x)^2) "d"x` is
Evaluate the following integral:
`int (x + 1)^2 log x "d"x`
Evaluate the following integral:
`int_0^3 (x dx)/(sqrt(x + 1)+ sqrt(5x + 1))`
