Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
उत्तर
Let I = `int 1/(sqrt"x" + "x")` dx
= `int 1/(sqrt"x" (1 + sqrt"x"))`dx
Put `1 + sqrt"x" = "t"`
∴ `1/(2sqrt"x") "dx" = "dt"`
∴ `1/sqrt"x"`dx = 2 dt
∴ I = `int (2 * "dt")/"t"`
`= 2 int 1/"t" * "dt"`
= 2 log | t | + c
∴ I = 2 log `|1 + sqrt"x"|` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
sin x ⋅ sin (cos x)
Integrate the functions:
`1/(1 - tan x)`
Evaluate the following integrals : `int tanx/(sec x + tan x)dx`
Evaluate the following integrals : `int(5x + 2)/(3x - 4).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
Evaluate: `int "x" * "e"^"2x"` dx
`int cos sqrtx` dx = _____________
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
