Advertisements
Advertisements
Question
Choose the correct alternative from the following.
`int "dx"/(("x" - "x"^2))`=
Options
log x – log (1 – x) + c
log (1 - x2) + c
- log x + log(1 - x) + c
log (x - x2) + c
Advertisements
Solution
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
RELATED QUESTIONS
Evaluate :`intxlogxdx`
Integrate the functions:
`(2cosx - 3sinx)/(6cos x + 4 sin x)`
Integrate the functions:
`(sin x)/(1+ cos x)^2`
Write a value of\[\int\frac{1}{1 + 2 e^x} \text{ dx }\].
Write a value of
Evaluate : `int ("e"^"x" (1 + "x"))/("cos"^2("x""e"^"x"))"dx"`
Integrate the following w.r.t. x : x3 + x2 – x + 1
Evaluate the following integral:
`int(4x + 3)/(2x + 1).dx`
Integrate the following function w.r.t. x:
x9.sec2(x10)
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x : `cosx/sin(x - a)`
Evaluate the following integral:
`int (3cosx)/(4sin^2x + 4sinx - 1).dx`
`int logx/(log ex)^2*dx` = ______.
Evaluate the following.
`int 1/("x" log "x")`dx
Choose the correct alternative from the following.
The value of `int "dx"/sqrt"1 - x"` is
Evaluate: `int "x" * "e"^"2x"` dx
Evaluate: `int sqrt(x^2 - 8x + 7)` dx
`int ((x + 1)(x + log x))^4/(3x) "dx" =`______.
If `int(cosx - sinx)/sqrt(8 - sin2x)dx = asin^-1((sinx + cosx)/b) + c`. where c is a constant of integration, then the ordered pair (a, b) is equal to ______.
The integral `int ((1 - 1/sqrt(3))(cosx - sinx))/((1 + 2/sqrt(3) sin2x))dx` is equal to ______.
Evaluate `int(1+ x + x^2/(2!)) dx`
Evaluate the following.
`int 1/(x^2+4x-5) dx`
Evaluate the following.
`int 1/(x^2 + 4x - 5)dx`
Evaluate:
`int 1/(1 + cosα . cosx)dx`
Evaluate `int (1 + x + x^2/(2!)) dx`
Evaluate `int(1+x+x^2/(2!))dx`
Evaluate.
`int (5x^2 -6x + 3)/(2x -3)dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
