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 x log x.
Integrate the function in `sin^(-1) ((2x)/(1+x^2))`.
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int x^3.logx.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x.cos^3x.dx`
Integrate the following functions w.r.t. x : `e^x .(1/x - 1/x^2)`
Integrate the following with respect to the respective variable : `(3 - 2sinx)/(cos^2x)`
Integrate the following w.r.t. x: `(1 + log x)^2/x`
Integrate the following w.r.t.x : `sqrt(x)sec(x^(3/2))*tan(x^(3/2))`
Integrate the following w.r.t.x : `(1)/(x^3 sqrt(x^2 - 1)`
Integrate the following w.r.t.x : e2x sin x cos x
Choose the correct alternative from the following.
`int (("e"^"2x" + "e"^"-2x")/"e"^"x") "dx"` =
`int sin4x cos3x "d"x`
Choose the correct alternative:
`int ("d"x)/((x - 8)(x + 7))` =
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
`int "e"^x x/(x + 1)^2 "d"x`
`int cot "x".log [log (sin "x")] "dx"` = ____________.
`int log x * [log ("e"x)]^-2` dx = ?
Evaluate the following:
`int_0^pi x log sin x "d"x`
The value of `int_0^(pi/2) log ((4 + 3 sin x)/(4 + 3 cos x)) dx` is
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.
If `int(x + (cos^-1 3x)^2)/sqrt(1 - 9x^2)dx = 1/α(sqrt(1 - 9x^2) + (cos^-1 3x)^β) + C`, where C is constant of integration , then (α + 3β) is equal to ______.
`int e^x [(2 + sin 2x)/(1 + cos 2x)]dx` = ______.
Find `int e^(cot^-1x) ((1 - x + x^2)/(1 + x^2))dx`.
Find `int e^x ((1 - sinx)/(1 - cosx))dx`.
Evaluate:
`int(1+logx)/(x(3+logx)(2+3logx)) dx`
Evaluate the following.
`intx^3/sqrt(1+x^4)`dx
