Advertisements
Advertisements
प्रश्न
Integrate the functions:
`sqrt(ax + b)`
Advertisements
उत्तर
Let `I = int sqrt(ax + b) dx`
Put ax + b = t
a dx = dt
`=> dx = 1/a dt`
Hence, `I = int 1/a sqrtt dt`
`= 1/a int t^(1/2) dt`
`= 1/a . 2/3 t^(3/2) + C`
`= 2/(3a) (ax + b)^(3/2) + C`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log |"x" +sqrt("x"^2 +"a"^2) | + "c"`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x:
`(1)/(sinx.cosx + 2cos^2x)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 + 2sin x - cosx)dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int 1/(7 + 6"x" - "x"^2)` dx
`int sqrt(1 + "x"^2) "dx"` =
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (sin4x)/(cos 2x) "d"x`
`int(1 - x)^(-2) dx` = ______.
Evaluate `int(3x^2 - 5)^2 "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int ("d"x)/(x(x^4 + 1))` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int cos^3x dx` = ______.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate `int 1/(x(x-1))dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
