Advertisements
Advertisements
प्रश्न
Evaluate `int 1/("x" ("x" - 1))` dx
Advertisements
उत्तर
Let I = `int 1/("x" ("x" - 1))` dx
`= int ("x" - "x" + 1)/("x"("x" - 1))` dx
`= int ("x" - ("x" - 1))/("x"("x" - 1))` dx
`= int (1/("x" - 1) - 1/"x")` dx
`= int 1/("x" - 1) "dx" - int 1/"x" "dx"`
`= log |"x" - 1| - log |"x"| + "c"`
∴ I = log `|("x" - 1)/"x"| + "c"`
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
`sin x/(1+ cos x)`
Write a value of
Write a value of
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : sin4x.cos3x
Integrate the following functions w.r.t. x : `((x - 1)^2)/(x^2 + 1)^2`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
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`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate: `int "e"^sqrt"x"` dx
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int(1 - x)^(-2)` dx = `(1 - x)^(-1) + c`
`int x^3 e^(x^2) dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate:
`int sin^2(x/2)dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(1 + x + x^2 / (2!))dx`
Evaluate `int1/(x(x - 1))dx`
