Advertisements
Advertisements
प्रश्न
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
पर्याय
`"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"`
उत्तर
`"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
संबंधित प्रश्न
Evaluate the following : `int x^2 sin 3x dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
Integrate the following functions w.r.t. x : `e^x/x [x (logx)^2 + 2 (logx)]`
Integrate the following functions w.r.t. x : cosec (log x)[1 – cot (log x)]
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Solve the following differential equation.
(x2 − yx2 ) dy + (y2 + xy2) dx = 0
Evaluate: `int "dx"/(25"x" - "x"(log "x")^2)`
`int sqrt(tanx) + sqrt(cotx) "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
`int log x * [log ("e"x)]^-2` dx = ?
`int "e"^x [x (log x)^2 + 2 log x] "dx"` = ______.
Find `int_0^1 x(tan^-1x) "d"x`
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Evaluate the following:
`int_0^pi x log sin x "d"x`
If u and v ore differentiable functions of x. then prove that:
`int uv dx = u intv dx - int [(du)/(d) intv dx]dx`
Hence evaluate `intlog x dx`
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.
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)dx`
Evaluate the following.
`intx^2e^(4x)dx`
