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
If `int_(-pi/2)^(pi/2)sin^4x/(sin^4x+cos^4x)dx`, then the value of I is:
(A) 0
(B) π
(C) π/2
(D) π/4
Integrate the function in x sin x.
Integrate the function in x cos-1 x.
Integrate the function in tan-1 x.
Integrate the function in x (log x)2.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
`int e^x sec x (1 + tan x) dx` equals:
Find :
`∫(log x)^2 dx`
Evaluate the following : `int sin θ.log (cos θ).dθ`
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 : `xsqrt(5 - 4x - x^2)`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Integrate the following functions w.r.t.x:
`e^(5x).[(5x.logx + 1)/x]`
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 tan(sin^-1 x)*dx` =
Choose the correct options from the given alternatives :
`int cos -(3)/(7)x*sin -(11)/(7)x*dx` =
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate the following.
`int (log "x")/(1 + log "x")^2` dx
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate `int 1/(x log x) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int [(log x - 1)/(1 + (log x)^2)]^2`dx = ?
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
State whether the following statement is true or false.
If `int (4e^x - 25)/(2e^x - 5)` dx = Ax – 3 log |2ex – 5| + c, where c is the constant of integration, then A = 5.
`intsqrt(1+x) dx` = ______
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`inte^x sinx dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
