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
Integrate the functions:
`sqrt(ax + b)`
Write a value of
Write a value of
Write a value of
Write a value of
Write a value of\[\int\frac{\sin x}{\cos^3 x} \text{ dx }\]
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sinx).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).
Evaluate the following.
`int 1/(x(x^6 + 1))` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
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: `int 1/(sqrt("x") + "x")` dx
Evaluate: `int "e"^sqrt"x"` dx
`int(1 - x)^(-2) dx` = ______.
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int(5x + 2)/(3x - 4) dx` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int cos^3x dx` = ______.
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int x^3 e^(x^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`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
