Advertisements
Advertisements
प्रश्न
Evaluate: `int "dx"/(5 - 16"x"^2)`
Advertisements
उत्तर
Let I = `int "dx"/(5 - 16"x"^2)`
`= int 1/(16(5/16 - "x"^2))` dx
`= 1/16 int 1/((sqrt5/4)^2 - "x"^2)` dx
`= 1/16 * 1/(2 sqrt5/4) log |(sqrt5/4 + "x")/(sqrt5/4 - "x")|` + c
∴ I = `1/(8sqrt5) log |(sqrt5 + 4"x")/(sqrt5 - 4"x")|` + c
APPEARS IN
संबंधित प्रश्न
Integrate the function in x2 log x.
`intx^2 e^(x^3) dx` equals:
Evaluate the following : `int x^2.log x.dx`
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following:
`int sec^3x.dx`
Evaluate the following : `int x.sin^2x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Integrate the following functions w.r.t. x : `((1 + sin x)/(1 + cos x)).e^x`
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Integrate the following w.r.t.x : cot–1 (1 – x + x2)
Integrate the following w.r.t.x : log (x2 + 1)
`int ("x" + 1/"x")^3 "dx"` = ______
Choose the correct alternative from the following.
`int (1 - "x")^(-2) "dx"` =
Evaluate: `int "dx"/(3 - 2"x" - "x"^2)`
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
Evaluate: `int "e"^"x"/(4"e"^"2x" -1)` dx
`int ("e"^xlog(sin"e"^x))/(tan"e"^x) "d"x`
`int (x^2 + x - 6)/((x - 2)(x - 1)) "d"x` = x + ______ + c
Evaluate `int 1/(x log x) "d"x`
Evaluate `int 1/(4x^2 - 1) "d"x`
`int 1/sqrt(x^2 - 8x - 20) "d"x`
Evaluate:
`int e^(ax)*cos(bx + c)dx`
Evaluate:
`inte^x sinx dx`
Evaluate:
`int (logx)^2 dx`
Evaluate the following:
`intx^3e^(x^2)dx`
Evaluate `int(1 + x + x^2/(2!))dx`.
Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3) dx`
