Advertisements
Advertisements
प्रश्न
Evaluate: `int "dx"/(5 - 16"x"^2)`
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 + 1) log x.
Evaluate the following : `int x^3.logx.dx`
Integrate the following functions w.r.t. x : `e^(2x).sin3x`
If f(x) = `sin^-1x/sqrt(1 - x^2), "g"(x) = e^(sin^-1x)`, then `int f(x)*"g"(x)*dx` = ______.
Evaluate the following.
`int "e"^"x" (1/"x" - 1/"x"^2)`dx
Evaluate the following.
`int "e"^"x" "x"/("x + 1")^2` dx
Evaluate: `int e^x/sqrt(e^(2x) + 4e^x + 13)` dx
`int(x + 1/x)^3 dx` = ______.
Evaluate `int 1/(4x^2 - 1) "d"x`
`int log x * [log ("e"x)]^-2` dx = ?
The value of `int_(- pi/2)^(pi/2) (x^3 + x cos x + tan^5x + 1) dx` is
The integral `int x cos^-1 ((1 - x^2)/(1 + x^2))dx (x > 0)` is equal to ______.
`intsqrt(1+x) dx` = ______
Evaluate `int(3x-2)/((x+1)^2(x+3)) dx`
Evaluate:
`int((1 + sinx)/(1 + cosx))e^x dx`
Prove that `int sqrt(x^2 - a^2)dx = x/2 sqrt(x^2 - a^2) - a^2/2 log(x + sqrt(x^2 - a^2)) + c`
Evaluate the following.
`intx^3 e^(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`
