Advertisements
Advertisements
प्रश्न
Evaluate the following.
`int 1/("x" log "x")`dx
Advertisements
उत्तर
Let I = `int 1/("x" log "x")`dx
Put log x = t
∴ `1/"x" "dx" = "dt'`
∴ I = `int 1/"t"` dt = log |t| + c
∴ I = log |log x| + c
Alternate Method:
Let I = `int 1/("x" * log "x")`dx
`= int (1//"x" "dx")/(log "x")`
∴ I = log |log x| + c .....`[because int ("f" '("x"))/("f"("x")) "dx" = log |"f"("x")| + "c"]`
APPEARS IN
संबंधित प्रश्न
Find : `int((2x-5)e^(2x))/(2x-3)^3dx`
Integrate the functions:
`(2x)/(1 + x^2)`
Integrate the functions:
`xsqrt(x + 2)`
Integrate the functions:
`1/(cos^2 x(1-tan x)^2`
Evaluate `int 1/(3+ 2 sinx + cosx) dx`
Write a value of\[\int\frac{1}{x \left( \log x \right)^n} \text { dx }\].
Evaluate: \[\int\frac{x^3 - 1}{x^2} \text{ dx}\]
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals: `int (2x - 7)/sqrt(4x - 1).dx`
Integrate the following function w.r.t. x:
`(10x^9 +10^x.log10)/(10^x + x^10)`
Integrate the following functions w.r.t. x : `int (1)/(cosx - sqrt(3)sinx).dx`
Evaluate the following.
`int (1 + "x")/("x" + "e"^"-x")` dx
Evaluate the following.
∫ (x + 1)(x + 2)7 (x + 3)dx
Evaluate the following.
`int ("2x" + 6)/(sqrt("x"^2 + 6"x" + 3))` dx
Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).
`int "e"^x[((x + 3))/((x + 4)^2)] "d"x`
State whether the following statement is True or False:
If `int x "f"(x) "d"x = ("f"(x))/2`, then f(x) = `"e"^(x^2)`
`int sin^-1 x`dx = ?
`int(5x + 2)/(3x - 4) dx` = ______
`int x/sqrt(1 - 2x^4) dx` = ______.
(where c is a constant of integration)
Evaluate `int_(logsqrt(2))^(logsqrt(3)) 1/((e^x + e^-x)(e^x - e^-x)) dx`.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int 1/("x"("x" - 1)) "dx"`
Evaluate the following.
`int x^3/(sqrt(1 + x^4))dx`
Evaluate:
`int sin^3x cos^3x dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4)dx`
Evaluate the following:
`int x^3/(sqrt(1 + x^4)) dx`
What is integration by substitution?
What is \[\int\cot t\,dt\] in the evaluation of \[\int\frac{\sin x}{\sin(x+a)}\,dx\]?
