Advertisements
Advertisements
प्रश्न
`int ("x" + 1/"x")^3 "dx"` = ______
पर्याय
`1/4 ("x" + 1/"x")^4` + c
`"x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c"`
`"x"^4/4 + "3x"^2/2 + 3 log "x" + 1/"x"^2 + "c"`
`("x" - "x"^-1)^3` + c
Advertisements
उत्तर
`int ("x" + 1/"x")^3 "dx"` = `bbunderline("x"^4/4 + "3x"^2/2 + 3 log "x" - 1/"2x"^2 + "c")`
Explanation:
Let I = `int ("x" + 1/"x")^3 "dx"`
`int ("x"^3 + "3x" + 3/"x" + 1/"x"^3)` dx
`= "x"^4/4 + 3 "x"^2/2 + 3 log |"x"| - 1/"2x"^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
If u and v are two functions of x then prove that
`intuvdx=uintvdx-int[du/dxintvdx]dx`
Hence evaluate, `int xe^xdx`
Integrate the function in x sin x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in (x2 + 1) log x.
Integrate the function in ex (sinx + cosx).
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Evaluate the following:
`int x.sin 2x. cos 5x.dx`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Choose the correct options from the given alternatives :
`int (1)/(x + x^5)*dx` = f(x) + c, then `int x^4/(x + x^5)*dx` =
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : log (x2 + 1)
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int 1/x "d"x` = ______ + c
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
`int(logx)^2dx` equals ______.
If `π/2` < x < π, then `intxsqrt((1 + cos2x)/2)dx` = ______.
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate:
`int e^(logcosx)dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
