Advertisements
Advertisements
प्रश्न
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Advertisements
उत्तर
`1/3`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int x^2/((x^2+2)(2x^2+1))dx`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(1)/(x(x^5 + 1)`
Integrate the following w.r.t. x: `(1)/(sinx + sin2x)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Integrate the following w.r.t. x : `(5*e^x)/((e^x + 1)(e^(2x) + 9)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
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 w.r.t. x: `(2x^2 - 1)/(x^4 + 9x^2 + 20)`
Integrate the following w.r.t.x:
`x^2/((x - 1)(3x - 1)(3x - 2)`
Evaluate: `int 1/("x"("x"^5 + 1))` dx
`int "dx"/(("x" - 8)("x" + 7))`=
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
`int x^2sqrt("a"^2 - x^6) "d"x`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (x^2 + x -1)/(x^2 + x - 6) "d"x`
Evaluate:
`int (5e^x)/((e^x + 1)(e^(2x) + 9)) dx`
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
`int (5(x^6 + 1))/(x^2 + 1) "d"x` = x5 – ______ x3 + 5x + c
Evaluate the following:
`int x^2/(1 - x^4) "d"x` put x2 = t
If `int dx/sqrt(16 - 9x^2)` = A sin–1 (Bx) + C then A + B = ______.
Evaluate.
`int (5x^2 - 6x + 3)/(2x - 3)dx`
When is a rational function called improper?
A proper rational function can be expressed as a sum of simpler rational functions called what?
Which decomposition corresponds to \[\frac{\mathrm{p}x^{2}+\mathrm{q}x+\mathrm{r}}{(x-\mathrm{a})(x^{2}+\mathrm{b}x+\mathrm{c})}\]?
What is done after long division, before writing the appropriate partial-fraction decomposition?
Which pair of equations is obtained by equating coefficients in \[5x-5=\mathrm{A}(x-3)+\mathrm{B}(x-2)\]?
Which decomposition is correct for \[\frac{x^{2}+1}{x^{2}-5x+6}\]?
