Advertisements
Advertisements
प्रश्न
Evaluate `int 1/("x" ("x" - 1))` dx
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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Write a value of\[\int\frac{\left( \tan^{- 1} x \right)^3}{1 + x^2} dx\]
Write a value of
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int sin x/cos^2x dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate the following.
`int 1/(4"x"^2 - 20"x" + 17)` dx
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int cot^2x "d"x`
`int cos^7 x "d"x`
Choose the correct alternative:
`int(1 - x)^(-2) dx` = ______.
`int (cos x)/(1 - sin x) "dx" =` ______.
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 ______.
`int (cos4x)/(sin2x + cos2x)dx` = ______.
