Advertisements
Advertisements
प्रश्न
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
पर्याय
log x – log (1 – x) + c
log (1 - x2) + c
- log x + log(1 - x) + c
log (x - x2) + c
Advertisements
उत्तर
log x – log (1 – x) + c
Explanation:
Let I = `int "dx"/(("x" - "x"^2))`
`= int 1/("x"(1 - "x"))` dx
`= int ((1 - "x")+"x")/("x"(1 - "x"))` dx
`= int (1/"x" + 1/"1 - x")` dx
`= log |"x"| + (log |1 - "x"|)/-1` + c
= log |x| - log |1 - x| + c
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`sqrt(sin 2x) cos 2x`
Write a value of
Write a value of\[\int e^x \left( \frac{1}{x} - \frac{1}{x^2} \right) dx\] .
Evaluate the following integrals:
`int(2)/(sqrt(x) - sqrt(x + 3)).dx`
Integrate the following functions w.r.t. x : `(1 + x)/(x.sin (x + log x)`
Integrate the following functions w.r.t. x : e3logx(x4 + 1)–1
Integrate the following functions w.r.t. x : `(20 + 12e^x)/(3e^x + 4)`
Evaluate the following : `int (1)/(1 + x - x^2).dx`
Evaluate the following : `int (1)/(cos2x + 3sin^2x).dx`
Evaluate the following integrals : `int (2x + 3)/(2x^2 + 3x - 1).dx`
Evaluate `int 1/(x (x - 1))` dx
Evaluate the following.
`int "x" sqrt(1 + "x"^2)` dx
Evaluate the following.
`int (20 - 12"e"^"x")/(3"e"^"x" - 4)`dx
Evaluate the following.
`int 1/(4x^2 - 20x + 17)` dx
Evaluate the following.
`int x/(4x^4 - 20x^2 - 3) dx`
To find the value of `int ((1 + log x) )/x dx` the proper substitution is ______.
`int e^x/x [x (log x)^2 + 2 log x]` dx = ______________
`int 2/(sqrtx - sqrt(x + 3))` dx = ________________
General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)
`int ("e"^x(x + 1))/(sin^2(x"e"^x)) "d"x` = ______.
If `int x^3"e"^(x^2) "d"x = "e"^(x^2)/2 "f"(x) + "c"`, then f(x) = ______.
Find `int dx/sqrt(sin^3x cos(x - α))`.
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Evaluate the following.
`int(20 - 12"e"^"x")/(3"e"^"x" - 4) "dx"`
Prove that:
`int 1/sqrt(x^2 - a^2) dx = log |x + sqrt(x^2 - a^2)| + c`.
`int x^3 e^(x^2) dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate the following.
`int1/(x^2+4x-5)dx`
Evaluate `int 1/(x(x-1)) dx`
