Advertisements
Advertisements
प्रश्न
Integrate the functions:
`((x+1)(x + logx)^2)/x`
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
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`(log x)^2/x`
Integrate the functions:
`sqrt(ax + b)`
Integrate the functions:
tan2(2x – 3)
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Write a value of
Write a value of
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Evaluate the following integrals : tan2x dx
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Integrate the following functions w.r.t. x : `(1)/(sinx.cosx + 2cos^2x)`
Integrate the following functions w.r.t. x : sin5x.cos8x
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int sinx/(sin 3x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int dx/(cosxsqrt(sin^2x - cos^2x))*dx` =
Choose the correct options from the given alternatives :
`int (e^(2x) + e^-2x)/e^x*dx` =
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate the following.
`int 1/(4"x"^2 - 1)` dx
Evaluate the following.
`int 1/(sqrt(3"x"^2 - 5))` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int log ("x"^2 + "x")` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
`int cos^3x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
`int x^3 e^(x^2) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate `int(5x^2-6x+3)/(2x-3) dx`
