Advertisements
Advertisements
Question
`int 1/(4x^2 - 1) dx` = ______.
Solution
`int 1/(4x^2 - 1) dx = bb(underline(1/4log |(2x - 1)/(2x + 1)|)`.
Explanation:
`int 1/(4x^2 - 1) dx = int 1/(4(x^2 - 1/4))dx`
= `1/4 int 1/(x^2 - (1/2)^2)dx`
= `1/4 log|(x - 1/2)/(x + 1/2)|`
= `1/4 log|(2x - 1)/(2x + 1)|`
∴ `int 1/(4x^2 - 1) dx = 1/4 log|(2x - 1)/(2x + 1)|`
APPEARS IN
RELATED QUESTIONS
Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`
Find `"dy"/"dx"`if, y = `"x"^("e"^"x")`
Find `"dy"/"dx"`if, y = `(1 + 1/"x")^"x"`
Find `"dy"/"dx"`if, y = `(log "x"^"x") + "x"^(log "x")`
Find `dy/dx`if, y = `(x)^x + (a^x)`.
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
Fill in the blank.
If y = y = [log (x)]2 then `("d"^2"y")/"dx"^2 =` _____.
The derivative of ax is ax log a.
Differentiate log (1 + x2) with respect to ax.
If xy = 2x – y, then `("d"y)/("d"x)` = ______
If u = ex and v = loge x, then `("du")/("dv")` is ______
State whether the following statement is True or False:
If y = 4x, then `("d"y)/("d"x)` = 4x
Find `("d"y)/("d"x)`, if y = xx + (7x – 1)x
Find `("d"y)/("d"x)`, if y = `x^(x^x)`
Find `("d"y)/("d"x)`, if y = `root(3)(((3x - 1))/((2x + 3)(5 - x)^2)`
If xa .yb = `(x + y)^((a + b))`, then show that `("d"y)/("d"x) = y/x`
Solve the following differential equations:
x2ydx – (x3 – y3)dy = 0
If y = (log x)2 the `dy/dx` = ______.
Find `dy/dx "if", y = x^(e^x)`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/dx` if, y = `x^(e^x)`
Find `dy/(dx) "if", y = x^(e^(x))`
Find `dy/(dx)` if, `y = x^(e^x)`
Find `dy/(dx)` if, `x = e^(3t), y = e^sqrtt`.
