Advertisements
Advertisements
प्रश्न
Integrate the functions:
`1/(x-sqrtx)`
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
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
(4x + 2) `sqrt(x^2 + x +1)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
cot x log sin x
Integrate the functions:
`1/(1 - tan x)`
Write a value of\[\int \log_e x\ dx\].
Write a value of\[\int\sqrt{9 + x^2} \text{ dx }\].
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals : `int(4x + 3)/(2x + 1).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `3^(cos^2x) sin 2x`
Integrate the following functions w.r.t. x : `(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
If f'(x) = x2 + 5 and f(0) = −1, then find the value of f(x).
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int dx/(1 + e^-x)` = ______
If f'(x) = `x + 1/x`, then f(x) is ______.
`int (logx)^2/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate the following
`int1/(x^2 +4x-5)dx`
Evaluate `int(1 + x + x^2/(2!))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`
