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
Show that: `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`
Evaluate : `int(x-3)sqrt(x^2+3x-18) dx`
Integrate the functions:
`1/(x + x log x)`
Integrate the functions:
`(x^3 - 1)^(1/3) x^5`
Integrate the functions:
`cos x /(sqrt(1+sinx))`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of
Write a value of
Integrate the following w.r.t. x : `(3x^3 - 2x + 5)/(xsqrt(x)`
Evaluate the following integrals:
tan2x dx
Integrate the following functions w.r.t. x : `(1)/(4x + 5x^-11)`
Integrate the following functions w.r.t. x : `(1)/(sqrt(x) + sqrt(x^3)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
`int (x^2 + x - 6)/((x - 2)(x - 1))dx = x` + ______ + c
Evaluate: `int sqrt("x"^2 + 2"x" + 5)` dx
`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________
`int sin^-1 x`dx = ?
`int "dx"/((sin x + cos x)(2 cos x + sin x))` = ?
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int dx/(2 + cos x)` = ______.
(where C is a constant of integration)
`int (logx)^2/x dx` = ______.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate the following.
`int(1)/(x^2 + 4x - 5)dx`
Evaluate the following:
`int x^3/(sqrt(1+x^4))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
