Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
पर्याय
log (3x) – log (9x) + c·
log (x) – (log 3) · log (log 9x) + c
log 9 – (log x) · log (log 3x) + c
log (x) + (log 3) · log (log 9x) + c
Advertisements
उत्तर
log (x) – (log 3) · log (log 9x) + c
[ Hint : `int (log3x)/(xlog(x))*dx = int (log((9x)/3))/(xlog(9x))*dx`
= `int (log (9x) - log3)/(xlog(9x))*dx`
= `int[1/x- (log3)/(xlog(9x))]*dx`
= `int 1/x*dx - (log3) int ((1/x))/(log (9x))*dx`
= log (x) – (log 3) · log (log 9x) + c].
APPEARS IN
संबंधित प्रश्न
Prove that: `int sqrt(a^2 - x^2) * dx = x/2 * sqrt(a^2 - x^2) + a^2/2 * sin^-1(x/a) + c`
Integrate the function in x log x.
Integrate the function in x sec2 x.
Integrate the function in ex (sinx + cosx).
Integrate the function in `e^x (1/x - 1/x^2)`.
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following : `int x^3.tan^-1x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following: `int logx/x.dx`
Evaluate the following : `int cos(root(3)(x)).dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `sqrt((x - 3)(7 - x)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following with respect to the respective variable : `(sin^6θ + cos^6θ)/(sin^2θ*cos^2θ)`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Evaluate the following.
∫ x log x dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate the following.
`int "e"^"x" [(log "x")^2 + (2 log "x")/"x"]` dx
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int "dx"/("x"[(log "x")^2 + 4 log "x" - 1])`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
`int "e"^x int [(2 - sin 2x)/(1 - cos 2x)]`dx = ______.
Find `int_0^1 x(tan^-1x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
Find the general solution of the differential equation: `e^((dy)/(dx)) = x^2`.
`int(logx)^2dx` equals ______.
`int_0^1 x tan^-1 x dx` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
`int1/(x+sqrt(x)) dx` = ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
The integrating factor of `ylogy.dx/dy+x-logy=0` is ______.
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int (logx)^2 dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
