Advertisements
Advertisements
प्रश्न
Integrate the functions:
`x/(9 - 4x^2)`
Advertisements
उत्तर
Let `I = int x/(9 - 4x^2)` dx
Put 9 - 4x2 = t
⇒ -8x dx = dt
∴ `I = -1/8 int dt/t`
`= -1/8 log |t| + C`
`= 1/8 log 1/ |t| + C`
`= 1/8 log 1/ (|9 - 4x^2|) +C`
APPEARS IN
संबंधित प्रश्न
Find `intsqrtx/sqrt(a^3-x^3)dx`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Integrate the functions:
`((x+1)(x + logx)^2)/x`
Write a value of
Write a value of
Write a value of\[\int e^{ax} \sin\ bx\ dx\]
Find : ` int (sin 2x ) /((sin^2 x + 1) ( sin^2 x + 3 ) ) dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `x^2/sqrt(9 - x^6)`
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int 1/("x" log "x")`dx
Evaluate the following.
`int ((3"e")^"2t" + 5)/(4"e"^"2t" - 5)`dt
Evaluate the following.
`int "x"^3/(16"x"^8 - 25)` dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate `int 1/((2"x" + 3))` dx
Evaluate: `int (2"e"^"x" - 3)/(4"e"^"x" + 1)` dx
`int x^2/sqrt(1 - x^6)` dx = ________________
`int logx/x "d"x`
`int "e"^(sin^-1 x) ((x + sqrt(1 - x^2))/(sqrt1 - x^2)) "dx" = ?`
If I = `int (sin2x)/(3x + 4cosx)^3 "d"x`, then I is equal to ______.
`int(sin2x)/(5sin^2x+3cos^2x) dx=` ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
If `int [log(log x) + 1/(logx)^2]dx` = x [f(x) – g(x)] + C, then ______.
Evaluate `int(1 + x + x^2/(2!) )dx`
Evaluate `int (1+x+x^2/(2!))dx`
Solve the following Evaluate.
`int(5x^2 - 6x + 3)/(2x - 3)dx`
`int "cosec"^4x dx` = ______.
Evaluate `int (1 + "x" + "x"^2/(2!))`dx
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
What is integration by substitution?
In \[\int\sin^3x\cos^2x\,dx\], which rewriting prepares the integrand for the substitution \[t=\cos x\]?
