Advertisements
Advertisements
प्रश्न
If f'(x) = `1/x + x` and f(1) = `5/2`, then f(x) = log x + `x^2/2` + ______ + c
Advertisements
उत्तर
2
APPEARS IN
संबंधित प्रश्न
Find : `int x^2/(x^4+x^2-2) dx`
Integrate the rational function:
`x/((x + 1)(x+ 2))`
Integrate the rational function:
`(3x + 5)/(x^3 - x^2 - x + 1)`
Integrate the following w.r.t. x : `(1)/(sin2x + cosx)`
Integrate the following w.r.t.x : `(1)/(2cosx + 3sinx)`
Integrate the following w.r.t.x : `sec^2x sqrt(7 + 2 tan x - tan^2 x)`
Evaluate:
`int (2x + 1)/(x(x - 1)(x - 4)) dx`.
`int "dx"/(("x" - 8)("x" + 7))`=
`int (2x - 7)/sqrt(4x- 1) dx`
`int "e"^x ((1 + x^2))/(1 + x)^2 "d"x`
`int (3x + 4)/sqrt(2x^2 + 2x + 1) "d"x`
`int x^3tan^(-1)x "d"x`
`int (x + sinx)/(1 - cosx) "d"x`
`int xcos^3x "d"x`
Choose the correct alternative:
`int sqrt(1 + x) "d"x` =
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 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
State whether the following statement is True or False:
For `int (x - 1)/(x + 1)^3 "e"^x"d"x` = ex f(x) + c, f(x) = (x + 1)2
Verify the following using the concept of integration as an antiderivative
`int (x^3"d"x)/(x + 1) = x - x^2/2 + x^3/3 - log|x + 1| + "C"`
Evaluate the following:
`int (x^2 "d"x)/((x^2 + "a"^2)(x^2 + "b"^2))`
The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 2 and the denominator is increased by 1, the denominator becomes eight times the numerator. Find the fraction.
Evaluate.
`int (5x^2 - 6x + 3) / (2x -3) dx`
If \[\int\frac{2x+3}{(x-1)(x^{2}+1)}\mathrm{d}x\] = \[=\log_{e}\left\{(x-1)^{\frac{5}{2}}\left(x^{2}+1\right)^{a}\right\}-\frac{1}{2}\tan^{-1}x+\mathrm{A}\] where A is an arbitrary constant, then the value of a is
Which partial-fraction decomposition is appropriate for \[\frac{\mathrm{p}x+\mathrm{q}}{(x-\mathrm{a})(x-\mathrm{b})}\]?
What should be checked before beginning partial-fraction decomposition?
For \[\frac{5x-5}{(x-2)(x-3)}=\frac{\mathrm{A}}{x-2}+\frac{\mathrm{B}}{x-3}\], which equation results after clearing denominators?
Which pair of equations is obtained by equating coefficients in \[5x-5=\mathrm{A}(x-3)+\mathrm{B}(x-2)\]?
What numerator is used for an irreducible quadratic factor?
