Advertisements
Advertisements
प्रश्न
Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.
Advertisements
उत्तर
Let I = `int (1)/(x.logx.log(logx)).dx`
= `int(1)/log(logx).(1)/(x.logx).dx`
Put log(log x) = t
∴ `(1)/logx.(1)/x.dx` = dt
∴ `(1)/(x.logx).dx` = dt
∴ I = `int (1)/t dt = log|t| + c`
= log|log (logx)| + c.
APPEARS IN
संबंधित प्रश्न
Evaluate: `int sqrt(tanx)/(sinxcosx) dx`
Integrate the functions:
sec2(7 – 4x)
Integrate the functions:
`cos sqrt(x)/sqrtx`
Integrate the functions:
`1/(1 + cot x)`
Evaluate: `int (2y^2)/(y^2 + 4)dx`
Write a value of
Write a value of
Write a value of\[\int \log_e x\ dx\].
Write a value of
Write a value of \[\int\frac{1 - \sin x}{\cos^2 x} \text{ dx }\]
Evaluate the following integrals:
`int (sin4x)/(cos2x).dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/sqrt(3x^2 + 5x + 7).dx`
Evaluate the following:
`int sinx/(sin 3x) dx`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int 1/(sqrt"x" + "x")` dx
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int ("e"^x(x - 1))/(x^2) "d"x` = ______
`int (2 + cot x - "cosec"^2x) "e"^x "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int x/(x + 2) "d"x`
State whether the following statement is True or False:
`int"e"^(4x - 7) "d"x = ("e"^(4x - 7))/(-7) + "c"`
Evaluate `int(3x^2 - 5)^2 "d"x`
`int x^3"e"^(x^2) "d"x`
`int cos^3x dx` = ______.
Write `int cotx dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
`int secx/(secx - tanx)dx` equals ______.
Evaluated the following
`int x^3/ sqrt (1 + x^4 )dx`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate `int 1/(x(x-1))dx`
Evaluate.
`int (5x^2-6x+3)/(2x-3)dx`
Evaluate the following:
`int (1) / (x^2 + 4x - 5) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate the following
`int x^3 e^(x^2) ` dx
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`int 1/ (x^2 + 4x - 5) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate `int (5x^2 - 6x + 3)/(2x - 3) dx`
