Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int "e"^"x" "x - 1"/("x + 1")^3` dx
उत्तर
Let I = `int "e"^"x" (("x - 1"))/("x + 1")^3 "dx" = int "e"^"x" (("x" + 1 - 1 - 1))/("x + 1")^3`dx
`= int "e"^"x" [("x + 1")/(("x + 1")^3) - 2/("x + 1")^3]` dx
`= int "e"^"x" [1/("x + 1")^2 - 2/("x + 1")^3]` dx
Put f(x) = `1/("x + 1")^2`
∴ f '(x) = `(-2)/("x + 1")^3`
∴ I = `int "e"^"x" ["f"("x") + "f" '("x")]` dx
`= "e"^"x" "f"("x") + "c"`
`= "e"^"x" xx 1/("x + 1")^2 + "c"`
∴ I = `"e"^"x"/("x + 1")^2 + "c"`
Notes
The answer in the textbook is incorrect.
APPEARS IN
संबंधित प्रश्न
Evaluate the following : `int x.sin^2x.dx`
Integrate the following functions w.r.t. x : `sqrt(4^x(4^x + 4))`
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int (sinx)/(1 + sin x) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int sin4x cos3x "d"x`
Evaluate `int (2x + 1)/((x + 1)(x - 2)) "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Evaluate: `int_0^(pi/4) (dx)/(1 + tanx)`
Solve: `int sqrt(4x^2 + 5)dx`
Find `int (sin^-1x)/(1 - x^2)^(3//2) dx`.
Find: `int e^(x^2) (x^5 + 2x^3)dx`.
`intsqrt(1+x) dx` = ______
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int (logx)^2 dx`
