Advertisements
Advertisements
प्रश्न
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Advertisements
उत्तर
Let I = `int "x - 1"/sqrt("x + 4")` dx
= `int (("x + 4") - 5)/sqrt("x + 4")` dx
= `int (sqrt"x + 4" - 5/(sqrt "x + 4"))` dx
`= int [("x + 4")^(1/2) - 5("x + 4")^(- 1/2)]` dx
`= ("x + 4")^(3/2)/(3/2) - 5 ("x + 4")^(1/2)/(1/2)` + c
∴ I = `2/3 ("x + 4")^(3/2) - 10 sqrt("x + 4")` + c
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`(e^(2x) - e^(-2x))/(e^(2x) + e^(-2x))`
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
Evaluate the following integrals:
`int (cos2x)/sin^2x dx`
Evaluate the following integrals : `intsqrt(1 - cos 2x)dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following : `int (1)/(7 + 2x^2).dx`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int cot^2x "d"x`
`int sin^-1 x`dx = ?
`int dx/(1 + e^-x)` = ______
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(3x + 1)/(2x^2 - 2x + 3)dx` equals ______.
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate:
`intsqrt(sec x/2 - 1)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
