Advertisements
Advertisements
प्रश्न
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Advertisements
उत्तर
Let `I = int ((x + 1) (x + log x)^2)/x dx`
`= int (x + log x)^2 (1 + 1/x) dx`
Put x + log x = t
⇒ `(1 + 1/x) dx = dt`
∴ `I = int t^2 dt = t^3/3 + C`
`= 1/3 (x + log x)^3 + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`e^(tan^(-1)x)/(1+x^2)`
`int (dx)/(sin^2 x cos^2 x)` equals:
Write a value of
Write a value of\[\int\text{ tan x }\sec^3 x\ dx\]
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t.x:
`(2sinx cosx)/(3cos^2x + 4sin^2 x)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : `(sinx + 2cosx)/(3sinx + 4cosx)`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int sqrt((2 + x)/(2 - x)).dx`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following : `int (logx)2.dx`
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
Evaluate `int (3"x"^2 - 5)^2` dx
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
`int 1/(cos x - sin x)` dx = _______________
`int (cos2x)/(sin^2x) "d"x`
`int(1 - x)^(-2) dx` = ______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int sec^6 x tan x "d"x` = ______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate.
`int(5"x"^2 - 6"x" + 3)/(2"x" - 3) "dx"`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
If f '(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
