Advertisements
Advertisements
प्रश्न
Integrate the function in `e^x (1/x - 1/x^2)`.
Advertisements
उत्तर
Let `I = inte^x (1/x - 1/x^2) dx`
`= int e^x {1/x + [d/dx (1/x)]} dx`
`= e^x xx 1/x + C = e^x/x + C` `...[∵ int e^x (f (x)+ f' (x)) dx = e^x f (x) + 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 (log x)2.
Integrate the function in `(xe^x)/(1+x)^2`.
`intx^2 e^(x^3) dx` equals:
`int e^x sec x (1 + tan x) dx` equals:
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int (t.sin^-1 t)/sqrt(1 - t^2).dt`
Integrate the following functions w.r.t. x : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
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 sin (log x)*dx` =
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
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))`
Integrate the following w.r.t.x : log (log x)+(log x)–2
Evaluate the following.
`int e^x (1/x - 1/x^2)`dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int 1/(4x + 5x^(-11)) "d"x`
`int sin4x cos3x "d"x`
`int ("d"x)/(x - x^2)` = ______
`int 1/x "d"x` = ______ + c
Evaluate `int 1/(4x^2 - 1) "d"x`
Evaluate the following:
`int ((cos 5x + cos 4x))/(1 - 2 cos 3x) "d"x`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate the following.
`int x^3 e^(x^2) dx`
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:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
