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
`int1/xlogxdx=...............`
(A)log(log x)+ c
(B) 1/2 (logx )2+c
(C) 2log x + c
(D) log x + c
Integrate the function in x log x.
Integrate the function in x2 log x.
Integrate the function in x (log x)2.
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:
Prove that:
`int sqrt(x^2 + a^2)dx = x/2 sqrt(x^2 + a^2) + a^2/2 log |x + sqrt(x^2 + a^2)| + c`
Find :
`∫(log x)^2 dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following : `int sin θ.log (cos θ).dθ`
Integrate the following functions w.r.t. x:
sin (log x)
Integrate the following functions w.r.t. x : `sec^2x.sqrt(tan^2x + tan x - 7)`
Integrate the following functions w.r.t. x : [2 + cot x – cosec2x]ex
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following with respect to the respective variable : `t^3/(t + 1)^2`
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `(1)/(xsin^2(logx)`
Integrate the following w.r.t.x : log (x2 + 1)
Evaluate the following.
`int x^3 e^(x^2)`dx
Evaluate the following.
`int e^x (1/x - 1/x^2)`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
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (("x"^3 + 3"x"^2 + 3"x" + 1))/("x + 1")^5 "dx"` =
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "dx"/(5 - 16"x"^2)`
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int 1/sqrt(2x^2 - 5) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int 1/(x^2 - "a"^2) "d"x` = ______ + c
`int"e"^(4x - 3) "d"x` = ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Find: `int e^x.sin2xdx`
`int 1/sqrt(x^2 - a^2)dx` = ______.
`int_0^1 x tan^-1 x dx` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Solution of the equation `xdy/dx=y log y` is ______
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int e^(logcosx)dx`
If ∫(cot x – cosec2 x)ex dx = ex f(x) + c then f(x) will be ______.
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
`∫ sin^(−1)` xdx is equal to ______.
