Advertisements
Advertisements
प्रश्न
Integrate the functions:
`(log x)^2/x`
Advertisements
उत्तर
Let `I = int (log x)^2/x` dx
Put log x = t
`1/x` dx = dt
Hence, `I = int t^2` dt
`I = t^3/3 + C`
`I = 1/3 (log x)^3 + C`
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫1/(cos^4x+sin^4x)dx`
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
`x^2/(2+ 3x^3)^3`
Integrate the functions:
`x/(9 - 4x^2)`
Integrate the functions:
cot x log sin x
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
The value of \[\int\frac{1}{x + x \log x} dx\] is
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals : `int (sin2x)/(cosx)dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`
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 : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `int (1)/(2 + cosx - sinx).dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sinx).dx`
`int logx/(log ex)^2*dx` = ______.
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate `int 1/(x (x - 1))` dx
`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
`int 1/sqrt((x - 3)(x + 2))` dx = ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int[ tan (log x) + sec^2 (log x)] dx= ` ______
`int sec^6 x tan x "d"x` = ______.
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Evaluate `int1/(x(x - 1))dx`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
Evaluate `int (1+x+x^2/(2!)) 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).
