Advertisements
Advertisements
प्रश्न
Evaluate: `int 1/(2"x" + 3"x" log"x")` dx
Advertisements
उत्तर
Let I = `int 1/(2"x" + 3"x" * log"x")` dx
`= int 1/("x"(2 + 3 log "x"))` dx
Put 2 + 3 log x = t
∴ `3 * 1/"x" "dx"` = dt
∴ `1/"x" "dx" = 1/3 "dt"`
∴ I = `1/3 int 1/"t" * "dt"`
`= 1/3` log |t| + c
∴ I = `1/3` log |2 + 3 log x| + c
APPEARS IN
संबंधित प्रश्न
Find `int((3sintheta-2)costheta)/(5-cos^2theta-4sin theta)d theta`.
Integrate the functions:
`1/(1 - tan x)`
Integrate the functions:
`sqrt(tanx)/(sinxcos x)`
Write a value of\[\int\frac{\sec^2 x}{\left( 5 + \tan x \right)^4} dx\]
Write a value of\[\int\frac{\sin x - \cos x}{\sqrt{1 + \sin 2x}} \text{ dx}\]
The value of \[\int\frac{\cos \sqrt{x}}{\sqrt{x}} dx\] is
Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`
Integrate the following functions w.r.t. x : `e^(3x)/(e^(3x) + 1)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Evaluate the following integrals : `int (3x + 4)/sqrt(2x^2 + 2x + 1).dx`
If f'(x) = 4x3 − 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Fill in the Blank.
`int (5("x"^6 + 1))/("x"^2 + 1)` dx = x4 + ______ x3 + 5x + c
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
State whether the following statement is True or False:
`int sqrt(1 + x^2) *x "d"x = 1/3(1 + x^2)^(3/2) + "c"`
`int (x^2 + 1)/(x^4 - x^2 + 1)`dx = ?
`int (sin (5x)/2)/(sin x/2)dx` is equal to ______. (where C is a constant of integration).
`int (x + sinx)/(1 + cosx)dx` is equal to ______.
`int sqrt(x^2 - a^2)/x dx` = ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`int1/(x^2+4x-5) dx`
Evaluate `int(1+x+(x^2)/(2!))dx`
Evaluate the following.
`int x^3/sqrt(1+x^4) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int "x"^3/sqrt(1 + "x"^4)` dx
Evaluate `int(5x^2-6x+3)/(2x-3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
