Advertisements
Advertisements
Question
Integrate the following with respect to x.
`1/(sqrt(x + 1) + sqrt(x - 1))`
Advertisements
Solution
`int (1/(sqrt(x + 1) + sqrt(x - 1))) "d"x`
= `int (1 xx (sqrt(x + 1) - sqrt(x - 1)))/((sqrt(x + 1) + sqrt(x - 1)) xx (sqrt(x + 1) - sqrt(x - 1))) "d"x`
= `int ((sqrt(x + 1) - sqrt(x - 1)))/((x + 1) - (x + 1)) "d"x`
= `int ((x + 1)^(1/2) - (x - 1)^(1/2))/(x + 1 - x + 1) "d"x`
= `1/2 [(x + 1)^(1/2 + 1)/((1/2 + 1)) - (x - 1)^(1/2 + 1)/((1/2 + 1))] + "c"`
= `1/2 [(x + 1)^(3/2)/((3/2)) - (x - 1)^(3/2)/((3/2))] + "c"`
= `1/2 [2/3 (x + 1)^(3/2) - 2/3 (x - 1)^(3/2)] + "c"`
= `2/2 [1/3 (x + 1)^(3/2) - 1/3 (x - 1)^(3/2)] + "c"`
= `1/2 [(x + 1)^(3/2) - (x - 1)^(3/2)] + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the following with respect to x.
`(8x + 13)/sqrt(4x + 7)`
Integrate the following with respect to x.
If f'(x) = `1/x` and f(1) = `pi/4`, then find f(x)
Integrate the following with respect to x.
If f'(x) = ex and f(0) = 2, then find f(x)
Integrate the following with respect to x.
x log x
Integrate the following with respect to x.
xn log x
Integrate the following with respect to x.
`("e"^(3logx))/(x^4 + 1)`
Integrate the following with respect to x.
`(x^("e" - 1) + "e"^(x - 1))/(x^"e" + "e"^x)`
Integrate the following with respect to x.
`1/sqrt(9x^2 - 7)`
Choose the correct alternative:
`int_2^4 ("d"x)/x` is
Evaluate the following integral:
`int_(-1)^1 x^2 "e"^(-2x) "d"x`
