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:
`(cos x)/((1-sinx)(2 - sin x))` [Hint: Put sin x = t]
`int (xdx)/((x - 1)(x - 2))` equals:
Evaluate : `∫(x+1)/((x+2)(x+3))dx`
Integrate the following w.r.t. x : `x^2/((x^2 + 1)(x^2 - 2)(x^2 + 3))`
Integrate the following w.r.t. x : `(12x^2 - 2x - 9)/((4x^2 - 1)(x + 3)`
Integrate the following w.r.t. x : `(5x^2 + 20x + 6)/(x^3 + 2x ^2 + x)`
Integrate the following w.r.t. x : `(2log x + 3)/(x(3 log x + 2)[(logx)^2 + 1]`
Integrate the following w.r.t.x : `x^2/sqrt(1 - x^6)`
Integrate the following w.r.t.x : `(1)/(sinx + sin2x)`
`int "dx"/(("x" - 8)("x" + 7))`=
For `int ("x - 1")/("x + 1")^3 "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)2.
Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx
`int "e"^(3logx) (x^4 + 1)^(-1) "d"x`
If f'(x) = `x - 3/x^3`, f(1) = `11/2` find f(x)
`int sec^3x "d"x`
`int ((2logx + 3))/(x(3logx + 2)[(logx)^2 + 1]) "d"x`
`int 1/x^3 [log x^x]^2 "d"x` = p(log x)3 + c Then p = ______
Evaluate `int x log x "d"x`
`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5) "dt"`
Evaluate the following:
`int_"0"^pi (x"d"x)/(1 + sin x)`
Evaluate: `int (dx)/(2 + cos x - sin x)`
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)
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
Value of ∫ `(x^2 + 1)/((x − 1)(x − 2))`dx is ______.
