Advertisements
Advertisements
प्रश्न
Integrate the functions:
`1/(x-sqrtx)`
Advertisements
उत्तर
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
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`(1+ log x)^2/x`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate `int (1 + x + x^2/(2!))`dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
`int sqrt(1 + "x"^2) "dx"` =
Evaluate: ∫ |x| dx if x < 0
`int (log x)/(log ex)^2` dx = _________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(1 - x)^(-2) dx` = ______.
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
`int (1 + x)/(x + "e"^(-x)) "d"x`
`int sin^-1 x`dx = ?
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`intx^3/sqrt(1+x^4)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).
Evaluate the following.
`int1/(x^2+4x-5)dx`
Which substitution is appropriate for \[\sqrt{\frac{\mathrm{a}-x}{\mathrm{a}+x}}\] or \[\sqrt{\frac{\mathrm{a}+x}{\mathrm{a}-x}}\]?
For \[\int\frac{\sin x}{\sin(x+a)}\,dx\], which substitution gives \[dx=dt\]?
