Advertisements
Advertisements
प्रश्न
`int 1/(xsin^2(logx)) "d"x`
Advertisements
उत्तर
Let I = `int 1/(x*sin^2(logx)) "d"x`
Put log x = t
∴ `1/x "d"x` = dt
∴ I = `int 1/(sin^2"t") "dt"`
= `int "cosec"^2"t"*"dt"`
= − cot t + c
∴ I = − cot (log x) + c
APPEARS IN
संबंधित प्रश्न
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Write a value of
Write a value of
Write a value of
Write a value of\[\int e^{ax} \left\{ a f\left( x \right) + f'\left( x \right) \right\} dx\] .
Evaluate the following integrals:
tan2x dx
Evaluate the following integrals: `int sin 4x cos 3x dx`
Integrate the following functions w.r.t. x : `(logx)^n/x`
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - 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 : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `sqrt(tanx)/(sinx.cosx)`
Integrate the following functions w.r.t. x : `(sin6x)/(sin 10x sin 4x)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following : `int (1)/(5 - 4x - 3x^2).dx`
Choose the correct options from the given alternatives :
`2 int (cos^2x - sin^2x)/(cos^2x + sin^2x)*dx` =
Evaluate `int (-2)/(sqrt("5x" - 4) - sqrt("5x" - 2))`dx
If f '(x) = `"x"^2/2 - "kx" + 1`, f(0) = 2 and f(3) = 5, find f(x).
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
Evaluate the following.
`int 1/(sqrt("x"^2 -8"x" - 20))` dx
`int sqrt(1 + "x"^2) "dx"` =
Choose the correct alternative from the following.
`int "x"^2 (3)^("x"^3) "dx"` =
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Evaluate: ∫ |x| dx if x < 0
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int (log x)/(log ex)^2` dx = _________
`int ("e"^(2x) + "e"^(-2x))/("e"^x) "d"x`
`int sqrt(x) sec(x)^(3/2) tan(x)^(3/2)"d"x`
`int (cos2x)/(sin^2x) "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"`
If f(x) = 3x + 6, g(x) = 4x + k and fog (x) = gof (x) then k = ______.
`int(5x + 2)/(3x - 4) dx` = ______
`int1/(4 + 3cos^2x)dx` = ______
`int (cos x)/(1 - sin x) "dx" =` ______.
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
The value of `int (sinx + cosx)/sqrt(1 - sin2x) dx` is equal to ______.
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Write `int cotx dx`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate `int (1+x+x^2/(2!)) dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate `int(1+x+x^2/(2!))dx`
