Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Advertisements
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:
`e^(2x+3)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Solve:
dy/dx = cos(x + y)
Write a value of\[\int\frac{1}{1 + e^x} \text{ dx }\]
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Show that : `int _0^(pi/4) "log" (1+"tan""x")"dx" = pi /8 "log"2`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Integrate the following with respect to the respective variable : `(x - 2)^2sqrt(x)`
Evaluate `int (3"x"^3 - 2sqrt"x")/"x"` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
State whether the following statement is True or False:
`int3^(2x + 3) "d"x = (3^(2x + 3))/2 + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int x^3"e"^(x^2) "d"x`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
