Advertisements
Advertisements
Question
Integrate the functions:
`1/(x(log x)^m), x > 0, m ne 1`
Advertisements
Solution
Let `I = int 1/(x (log x)^m) dx`
Put log x = t
`1/x dx = dt`
`therefore I = int dt/t^m`
`= int t^(-m) dt = (t^(-m + 1)/(- m + 1)) + C`
`= (log x)^(- m + 1)/(1 - m) + C`
APPEARS IN
RELATED QUESTIONS
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate :
`int(sqrt(cotx)+sqrt(tanx))dx`
Integrate the functions:
sin (ax + b) cos (ax + b)
Evaluate: `int 1/(x(x-1)) dx`
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Write a value of
Write a value of\[\int\sqrt{x^2 - 9} \text{ dx}\]
\[\int\frac{\sin x + 2 \cos x}{2 \sin x + \cos x} \text{ dx }\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int sin x/cos^2x dx`
Evaluate the following integrals: `int(x - 2)/sqrt(x + 5).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
Evaluate the following integrals : `int cos^2x.dx`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Evaluate the following : `int (1)/sqrt(11 - 4x^2).dx`
Evaluate the following : `int (1)/sqrt(x^2 + 8x - 20).dx`
Integrate the following functions w.r.t. x : `int (1)/(3 - 2cos 2x).dx`
Evaluate the following integrals : `int sqrt((9 - x)/x).dx`
Evaluate the following integrals : `int sqrt((e^(3x) - e^(2x))/(e^x + 1)).dx`
Choose the correct options from the given alternatives :
`int sqrt(cotx)/(sinx*cosx)*dx` =
Choose the correct options from the given alternatives :
`int f x^x (1 + log x)*dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Integrate the following w.r.t.x: `(3x + 1)/sqrt(-2x^2 + x + 3)`
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int sqrt(x^2 + 2x + 5)` dx = ______________
`int (cos2x)/(sin^2x) "d"x`
`int(log(logx))/x "d"x`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate `int1/(x(x-1))dx`
Evaluate the following.
`int1/(x^2 + 4x-5)dx`
