Advertisements
Advertisements
Question
Integrate the functions:
`1/(x-sqrtx)`
Advertisements
Solution
Let `I = int 1/(x - sqrtx) dx`
`= int 1/(sqrt x - (sqrtx - 1)) dx`
Taking `sqrt x - 1 = t`
`1/(2 sqrt x) dx = dt`
or `1/sqrt x dx = 2 dt`
Hence, `I = int 1/2. 2 dt = 2 int1/t dt`
= 2 log t + C
`= 2 log (sqrtx - 1) = C`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`
Integrate the functions:
tan2(2x – 3)
Write a value of\[\int \cos^4 x \text{ sin x dx }\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Integrate the following w.r.t. x:
`2x^3 - 5x + 3/x + 4/x^5`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(4e^x - 25)/(2e^x - 5)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int (e^x(x - 1))/x^2*dx` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
State whether the following statement is True or False.
If ∫ x f(x) dx = `("f"("x"))/2`, then find f(x) = `"e"^("x"^2)`
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
Evaluate: ∫ |x| dx if x < 0
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (log x)/(log ex)^2` dx = _________
`int (sin4x)/(cos 2x) "d"x`
`int ("e"^(3x))/("e"^(3x) + 1) "d"x`
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int sin^-1 x`dx = ?
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If f'(x) = `x + 1/x`, then f(x) is ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
If `int sinx/(sin^3x + cos^3x)dx = α log_e |1 + tan x| + β log_e |1 - tan x + tan^2x| + γ tan^-1 ((2tanx - 1)/sqrt(3)) + C`, when C is constant of integration, then the value of 18(α + β + γ2) is ______.
Evaluate `int 1/(x(x-1))dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int 1/(x(x-1))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
