Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(1+ log x)^2/x`
उत्तर
Let `I = int (1 + log x)^2/x dx`
Put 1 + log x = t
`1/x dt = dt`
Hence, `I = int t^2` dt
`= t^3/3 + C`
`= 1/3 (1 + log x)^3 + C`
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
sin (ax + b) cos (ax + b)
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`1/(1 - tan x)`
Write a value of
Integrate the following w.r.t. x:
`3 sec^2x - 4/x + 1/(xsqrt(x)) - 7`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Integrate the following functions w.r.t. x : tan 3x tan 2x tan x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following.
`int (3"e"^"x" + 4)/(2"e"^"x" - 8)`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3)dx`
Evaluate the following.
`int 1/("a"^2 - "b"^2 "x"^2)` dx
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int sqrt(x^2 + 2x + 5)` dx = ______________
If `int 1/(x + x^5)` dx = f(x) + c, then `int x^4/(x + x^5)`dx = ______
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int sqrt(("e"^(3x) - "e"^(2x))/("e"^x + 1)) "d"x`
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int dx/(1 + e^-x)` = ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int ("d"x)/(sinx cosx + 2cos^2x)` = ______.
`int secx/(secx - tanx)dx` equals ______.
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int sqrt((a - x)/x) dx`
Evaluate:
`int sin^2(x/2)dx`
If f'(x) = 4x3- 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
`int 1/(sin^2x cos^2x)dx` = ______.
Evaluate:
`intsqrt(3 + 4x - 4x^2) dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
