Advertisements
Advertisements
प्रश्न
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Advertisements
उत्तर
Let I = `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
`= -2 int 1/(sqrt("5x" - 4) - sqrt("5x" - 2)) xx (sqrt("5x" - 4) + sqrt("5x" - 2))/(sqrt("5x" - 4) + sqrt("5x" - 2))`dx
`= - 2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/(("5x" - 4) - ("5x" - 2))` dx
`= -2 int (sqrt("5x" - 4) + sqrt("5x" - 2))/-2` dx
`= int [("5x" - 4)^(1/2) + ("5x" - 2)^(1/2)]`dx
`= int ("5x" - 4)^(1/2) "dx" + int ("5x" - 2)^(1/2)` dx
`= ("5x" - 4)^(3/2)/(3/2) xx 1/5 + ("5x" - 2)^(3/2)/(3/2) xx 1/5` + c
∴ I = `2/15 [("5x" - 4)^(3/2) + ("5x" - 2)^(3/2)]` + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Solve:
dy/dx = cos(x + y)
Write a value of
Write a value of\[\int\frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} dx\]
Write a value of
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following functions w.r.t. x : `(e^(2x) + 1)/(e^(2x) - 1)`
Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/sqrt(8 - 3x + 2x^2).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int (cos2x - 1)/(cos2x + 1)*dx` =
Evaluate `int (3"x"^2 - 5)^2` dx
Fill in the Blank.
`int 1/"x"^3 [log "x"^"x"]^2 "dx" = "P" (log "x")^3` + c, then P = _______
`int x^3"e"^(x^2) "d"x`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
The general solution of the differential equation `(1 + y/x) + ("d"y)/(d"x)` = 0 is ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
`int 1/(sinx.cos^2x)dx` = ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5) dx`
`int dx/((x+2)(x^2 + 1))` ...(given)
`1/(x^2 +1) dx = tan ^-1 + c`
`int 1/(sin^2x cos^2x)dx` = ______.
The value of `int ("d"x)/(sqrt(1 - x))` is ______.
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
