Advertisements
Advertisements
प्रश्न
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
पर्याय
`log ("cosec"x - cotx) + tan(x/2) + c`
sin 2x – cos x + c
`log (secx + tanx) - cot(x/2) + c`
cos 2x – sin x + c
Advertisements
उत्तर
`log (secx + tanx) - cot(x/2) + c`
[ Hint : `int 1/(cosx - cos^2x)*dx`
= `int 1/(cosx(1 - cosx))*dx`
= `int ((1 - cosx) + cosx)/(cosx(1 - cosx))*dx`
= `int (1/cosx + 1/(1 - cosx))*dx`
= `int [sec x + 1/2 "cosec"^2(x/2)]*dx`
= `log|secx + tanx|1/2((-cotx/2))/(1/2) + c`
= `log|secx + tanx| - cot(x/2) + c`].
APPEARS IN
संबंधित प्रश्न
Integrate the function in x2 log x.
Integrate the function in x cos-1 x.
Integrate the function in x sec2 x.
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Evaluate the following:
`int x.sin 2x. cos 5x.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:
sin (log x)
Integrate the following functions w.r.t. x : `(x + 1) sqrt(2x^2 + 3)`
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t.x : log (x2 + 1)
Integrate the following w.r.t.x : sec4x cosec2x
Evaluate the following.
`int x^2 e^4x`dx
Evaluate the following.
`int x^2 *e^(3x)`dx
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int "dx"/("9x"^2 - 25)`
`int (sinx)/(1 + sin x) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
`int sqrt(tanx) + sqrt(cotx) "d"x`
Choose the correct alternative:
`intx^(2)3^(x^3) "d"x` =
`int 1/x "d"x` = ______ + c
Evaluate `int 1/(x log x) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
∫ log x · (log x + 2) dx = ?
`int log x * [log ("e"x)]^-2` dx = ?
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
`int(logx)^2dx` equals ______.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int (logx)^2 dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
If u and v are two differentiable functions of x, then prove that `intu*v*dx = u*intv dx - int(d/dx u)(intv dx)dx`. Hence evaluate: `intx cos x dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3e^(x^2) dx`
Evaluate:
`int x^2 cos x dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
Evaluate the following.
`intx^2e^(4x)dx`
Evaluate the following.
`intx^3/(sqrt(1 + x^4))dx`
The value of `int (x sin^-1)/(sqrt(1 - x^2)) dx` is equal to:
