Advertisements
Advertisements
प्रश्न
`int (xdx)/((x - 1)(x - 2))` equals:
विकल्प
`log |(x - 1)^2/(x - 2)| + C`
`log |(x - 2)^2/(x - 1)| + C`
`log |((x - 1^2)/(x - 2))| + C`
log|(x - 1)(x - 2) + C
Advertisements
उत्तर
`log abs ((x - 2)^2/(x - 1)) + C`
Explanation:
Let `I = int x/ ((x - 1) (x - 2)) dx`
`= int [(-1)/ (x - 1) + 2/ (x - 2)] dx`
= - log (x - 1) + 2 log (x - 2) + C
`= log |(x - 2)^2/(x - 1)| + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Integrate the rational function:
`(3x - 1)/((x - 1)(x - 2)(x - 3))`
Integrate the rational function:
`x/((x -1)^2 (x+ 2))`
Integrate the rational function:
`(5x)/((x + 1)(x^2 - 4))`
Integrate the rational function:
`(x^3 + x + 1)/(x^2 -1)`
Integrate the rational function:
`1/(x(x^n + 1))` [Hint: multiply numerator and denominator by xn − 1 and put xn = t]
Integrate the rational function:
`((x^2 +1)(x^2 + 2))/((x^2 + 3)(x^2+ 4))`
Integrate the rational function:
`(2x)/((x^2 + 1)(x^2 + 3))`
`int (dx)/(x(x^2 + 1))` equals:
Integrate the following w.r.t. x:
`(6x^3 + 5x^2 - 7)/(3x^2 - 2x - 1)`
Integrate the following w.r.t. x : `(3x - 2)/((x + 1)^2(x + 3)`
Integrate the following w.r.t. x : `(1)/(x(1 + 4x^3 + 3x^6)`
Choose the correct options from the given alternatives :
If `int tan^3x*sec^3x*dx = (1/m)sec^mx - (1/n)sec^n x + c, "then" (m, n)` =
Integrate the following with respect to the respective variable : `cot^-1 ((1 + sinx)/cosx)`
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x: `(x + 5)/(x^3 + 3x^2 - x - 3)`
Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx
`int (2x - 7)/sqrt(4x- 1) dx`
`int x^7/(1 + x^4)^2 "d"x`
`int (sinx)/(sin3x) "d"x`
`int sin(logx) "d"x`
`int (sin2x)/(3sin^4x - 4sin^2x + 1) "d"x`
`int (3"e"^(2x) + 5)/(4"e"^(2x) - 5) "d"x`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
Choose the correct alternative:
`int ((x^3 + 3x^2 + 3x + 1))/(x + 1)^5 "d"x` =
If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c
`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5) "dt"`
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
If f(x) = `int(3x - 1)x(x + 1)(18x^11 + 15x^10 - 10x^9)^(1/6)dx`, where f(0) = 0, is in the form of `((18x^α + 15x^β - 10x^γ)^δ)/θ`, then (3α + 4β + 5γ + 6δ + 7θ) is ______. (Where δ is a rational number in its simplest form)
`int 1/(x^2 + 1)^2 dx` = ______.
Evaluate:
`int(2x^3 - 1)/(x^4 + x)dx`
What should be checked before beginning partial-fraction decomposition?
Which factorisation is correct for \[x^{2}-5x+6\]?
Evaluate \[\int\frac{x^{2}+1}{x^{2}-5x+6}\,dx\].
