Advertisements
Advertisements
प्रश्न
Evaluate `int "x - 1"/sqrt("x + 4")` dx
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 `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Integrate the functions:
sin (ax + b) cos (ax + b)
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : `int sinx/(1 + sinx)dx`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(2 + 3tanx)`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int cot^2x "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
