Advertisements
Advertisements
Question
Evaluate the following.
`int "e"^"x" (1/"x" - 1/"x"^2)`dx
Solution
Let I = `int "e"^"x" (1/"x" - 1/"x"^2)`dx
Put f(x) = `1/"x"`
∴ f '(x) = `1/"x"`
∴ I = `int "e"^"x" ["f"("x") + "f" '("x")]` dx
`= "e"^"x" * "f"("x") + "c"`
∴ I = `"e"^"x" * 1/"x" + "c"`
Notes
The answer in the textbook is incorrect.
APPEARS IN
RELATED QUESTIONS
Integrate : sec3 x w. r. t. x.
`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^2e^x`.
Integrate the function in x sec2 x.
Integrate the function in tan-1 x.
Integrate the function in `(xe^x)/(1+x)^2`.
Evaluate the following : `int x^2tan^-1x.dx`
Integrate the following functions w.r.t. x : `e^(sin^-1x)*[(x + sqrt(1 - x^2))/sqrt(1 - x^2)]`
Integrate the following functions w.r.t. x : `log(1 + x)^((1 + x)`
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Integrate the following with respect to the respective variable : cos 3x cos 2x cos x
Evaluate the following.
`int [1/(log "x") - 1/(log "x")^2]` dx
`int (sinx)/(1 + sin x) "d"x`
`int ["cosec"(logx)][1 - cot(logx)] "d"x`
`int "e"^x x/(x + 1)^2 "d"x`
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4))dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
The value of `int e^x((1 + sinx)/(1 + cosx))dx` is ______.
