Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(logx)^n/x`
Advertisements
उत्तर
Let I = `int (logx)^n/x.dx`
Put log x = t.
∴ `(1)/x.dx = dt`
∴ I = `int t^n dt`
= `(t^(n + 1))/(n + 1) + c`
= `(1)/(n + 1).(logx)^(n + 1) + c`.
APPEARS IN
संबंधित प्रश्न
Find the particular solution of the differential equation x2dy = (2xy + y2) dx, given that y = 1 when x = 1.
Integrate the functions:
`1/(x-sqrtx)`
Integrate the functions:
`x/(sqrt(x+ 4))`, x > 0
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Integrate the functions:
`sin x/(1+ cos x)`
`(10x^9 + 10^x log_e 10)/(x^10 + 10^x) dx` equals:
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`
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:
`x^5sqrt(a^2 + x^2)`
Integrate the following functions w.r.t.x:
`(5 - 3x)(2 - 3x)^(-1/2)`
Integrate the following functions w.r.t. x : `(1)/(x(x^3 - 1)`
Integrate the following functions w.r.t. x : `(cos3x - cos4x)/(sin3x + sin4x)`
Integrate the following functions w.r.t.x:
cos8xcotx
Evaluate the following : `int sqrt((9 + x)/(9 - x)).dx`
Evaluate the following : `int (1)/(4 + 3cos^2x).dx`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
If f '(x) = `1/"x" + "x"` and f(1) = `5/2`, then f(x) = log x + `"x"^2/2` + ______
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int(5x + 2)/(3x - 4) dx` = ______
If `tan^-1x = 2tan^-1((1 - x)/(1 + x))`, then the value of x is ______
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `intsinx/(sinx - cosx)dx` equals ______.
Evaluate `int 1/("x"("x" - 1)) "dx"`
`int x^3 e^(x^2) dx`
If f ′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
`int (x + 1)/(x(1 + xe^x)) dx` is equal to
Which standard substitution is used for \[\sqrt{\mathrm{a}^2-x^2}\], \[\frac{1}{\sqrt{\mathrm{a}^2-x^2}}\], or \[\mathrm{a}^2-x^2\]?
After putting \[t=\cos x\], which integral is obtained from \[\int\sin^2x\cos^2x(\sin x)\,dx\]?
