Advertisements
Advertisements
प्रश्न
`int "e"^x x/(x + 1)^2 "d"x`
Advertisements
उत्तर
Let I = `int "e"^x(x/((x + 1)^2))"d"x`
= `int"e"^x (((x + 1) - 1)/(x + 1)^2)"d"x`
= `int"e"^x ((x + 1)/(x + 1)^2 - 1/(x + 1)^2)"d"x`
= `int"e"^x (1/(x + 1) - 1/(x + 1)^2)"d"x`
Put f(x) = `1/(x + 1)`
∴ f'(x) = `(-1)/(x + 1)^2`
∴ I = `int"e"^x["f"(x) + "f'"(x)]"d"x`
= `"e"^x*"f"(x) + "c"`
∴ I = `"e"^x (1/(x + 1)) + "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
`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 sin 3x.
Integrate the function in x2 log x.
Integrate the function in `(x cos^(-1) x)/sqrt(1-x^2)`.
Integrate the function in tan-1 x.
Integrate the function in (x2 + 1) log x.
Find :
`∫(log x)^2 dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following: `int x.sin^-1 x.dx`
Evaluate the following: `int logx/x.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following functions w.r.t. x : `[x/(x + 1)^2].e^x`
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 + log x)^2/x`
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
Evaluate: `int "dx"/sqrt(4"x"^2 - 5)`
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int sqrt(tanx) + sqrt(cotx) "d"x`
`int"e"^(4x - 3) "d"x` = ______ + c
`int log x * [log ("e"x)]^-2` dx = ?
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Evaluate:
`intcos^-1(sqrt(x))dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int1/(x^2 + 25)dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
