Advertisements
Advertisements
प्रश्न
Integrate the function in `(xe^x)/(1+x)^2`.
उत्तर
Let `I = int (xe^x)/((1 + x)^2) dx`
`= int ((x + 1 - 1) e^x)/((1 + x)^2) dx`
`= int 1/((1 + x)) . e^x dx - (e^x - 1)/((1 + x)^2) dx`
`= 1/((1 + x)). e^x - int (-1)/((1 + x^2)).e^x dx - int e^x/((1 + x^2)) dx + C`
`= e^x/(1 + x) + int e^x/((1 + x)^2) dx - int e^x/((1 + x)^2) dx + C`
`= e^x/(1 + x) + C`
APPEARS IN
संबंधित प्रश्न
Integrate the function in x sec2 x.
Integrate the function in x (log x)2.
Integrate the function in ex (sinx + cosx).
Evaluate the following : `int x^2tan^-1x.dx`
Integrate the following functions w.r.t. x:
sin (log x)
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 : `sqrt(2x^2 + 3x + 4)`
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` =
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: Find the primitive of `1/(1 + "e"^"x")`
Evaluate: `int ("ae"^("x") + "be"^(-"x"))/("ae"^("x") - "be"^(−"x"))` dx
`int 1/sqrt(2x^2 - 5) "d"x`
`int (cos2x)/(sin^2x cos^2x) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
∫ log x · (log x + 2) dx = ?
`int_0^"a" sqrt("x"/("a" - "x")) "dx"` = ____________.
Find `int_0^1 x(tan^-1x) "d"x`
`int "dx"/(sin(x - "a")sin(x - "b"))` is equal to ______.
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.
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
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(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate:
`int (logx)^2 dx`
Evaluate `int tan^-1x dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4) dx`
Evaluate the following.
`intx^3e^(x^2) dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x)
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
