Advertisements
Advertisements
Question
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
Options
`"e"^"x" - 1/(3"e"^"3x")` + c
`"e"^"x" + 1/(3"e"^"3x")` + c
`"e"^"-x" + 1/(3"e"^"3x")` + c
`"e"^"-x" + 1/(3"e"^"3x") + "c"`
Advertisements
Solution
`"e"^"x" - 1/(3"e"^"3x")` + c
Explanation:
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx" = int ("e"^"x" + "e"^(-3"x"))` dx
`= "e"^"x" - 1/3 "e"^(-3"x") + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the function in `(xe^x)/(1+x)^2`.
Integrate the function in e2x sin x.
Evaluate the following:
`int x^2 sin 3x dx`
Evaluate the following: `int x.sin^-1 x.dx`
Integrate the following functions w.r.t.x:
`e^-x cos2x`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Choose the correct options from the given alternatives :
`int tan(sin^-1 x)*dx` =
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 e^x (1/x - 1/x^2)`dx
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/("9x"^2 - 25)`
`int (sin(x - "a"))/(cos (x + "b")) "d"x`
Evaluate `int 1/(4x^2 - 1) "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"` = ____________.
Evaluate the following:
`int_0^1 x log(1 + 2x) "d"x`
`int x/((x + 2)(x + 3)) dx` = ______ + `int 3/(x + 3) dx`
Evaluate the following.
`int x^3 e^(x^2) dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Complete the following activity:
`int_0^2 dx/(4 + x - x^2) `
= `int_0^2 dx/(-x^2 + square + square)`
= `int_0^2 dx/(-x^2 + x + 1/4 - square + 4)`
= `int_0^2 dx/ ((x- 1/2)^2 - (square)^2)`
= `1/sqrt17 log((20 + 4sqrt17)/(20 - 4sqrt17))`
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`
Evaluate `int (1 + x + x^2/(2!))dx`
Evaluate:
`inte^x "cosec" x(1 - cot x)dx`
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
