Advertisements
Advertisements
Question
Evaluate `int 1/(4x^2 - 1) "d"x`
Advertisements
Solution
Let I = `int ("d"x)/(4x^2 - 1)`
= `1/4 int ("d"x)/(x^2 - 1/4)`
= `1/4 int ("d"x)/(x^2 - (1/2)^2`
= `1/4 xx 1/(2 xx 1/2) log |(x - 1/2)/(x + 1/2)| + "c"`
∴ I = `1/4 log|(2x - 1)/(2x + 1)| + "c"`
APPEARS IN
RELATED QUESTIONS
Integrate the function in (x2 + 1) log x.
Integrate the function in `e^x (1 + sin x)/(1+cos x)`.
Evaluate the following : `int x^2tan^-1x.dx`
Evaluate the following : `int e^(2x).cos 3x.dx`
Evaluate the following : `int x^2*cos^-1 x*dx`
Evaluate the following : `int cos sqrt(x).dx`
Integrate the following functions w.r.t. x: `sqrt(x^2 + 2x + 5)`.
Choose the correct options from the given alternatives :
`int (log (3x))/(xlog (9x))*dx` =
Choose the correct options from the given alternatives :
`int (sin^m x)/(cos^(m+2)x)*dx` =
Choose the correct options from the given alternatives :
`int (1)/(cosx - cos^2x)*dx` =
Choose the correct options from the given alternatives :
`int [sin (log x) + cos (log x)]*dx` =
Integrate the following w.r.t.x : e2x sin x cos x
`int ("x" + 1/"x")^3 "dx"` = ______
Evaluate: `int "dx"/(5 - 16"x"^2)`
`int (cos2x)/(sin^2x cos^2x) "d"x`
State whether the following statement is True or False:
If `int((x - 1)"d"x)/((x + 1)(x - 2))` = A log|x + 1| + B log|x – 2|, then A + B = 1
∫ log x · (log x + 2) dx = ?
Evaluate the following:
`int (sin^-1 x)/((1 - x)^(3/2)) "d"x`
Find: `int (2x)/((x^2 + 1)(x^2 + 2)) dx`
`int(logx)^2dx` equals ______.
`int (sin^-1 sqrt(x) + cos^-1 sqrt(x))dx` = ______.
Evaluate `int tan^-1x dx`
Evaluate the following.
`intx^3 e^(x^2) dx`
`∫ sin^(−1)` xdx is equal to ______.
Under the LIATE rule, which type of function has priority \(L\)?
Which function is an example under priority \(I\) in the LIATE rule?
Using \[t=1-x^2,\] what is \[\int \frac{x\,dx}{\sqrt{1-x^2}}?\]
When applying integration by parts to \(\log x\) and inverse trig, what should they be multiplied by?
