Advertisements
Advertisements
प्रश्न
`int 1/(4x^2 - 1) dx` = ______.
Advertisements
उत्तर
`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
संबंधित प्रश्न
Find `"dy"/"dx"`if, y = `"x"^("x"^"2x")`
Find `"dy"/"dx"`if, y = (2x + 5)x
Find `"dy"/"dx"`if, y = `root(3)(("3x" - 1)/(("2x + 3")(5 - "x")^2))`
Find `dy/dx`if, y = `(x)^x + (a^x)`.
If y = elogx then `dy/dx` = ?
Fill in the blank.
If x = t log t and y = tt, then `"dy"/"dx"` = ____
If y = x log x, then `(d^2y)/dx^2`= ______.
State whether the following is True or False:
The derivative of `log_ax`, where a is constant is `1/(x.loga)`.
State whether the following is True or False:
If y = log x, then `"dy"/"dx" = 1/"x"`
State whether the following is True or False:
If y = e2, then `"dy"/"dx" = 2"e"`
Choose the correct alternative:
If y = (x )x + (10)x, then `("d"y)/("d"x)` = ?
Find `("d"y)/("d"x)`, if x = `sqrt(1 + "u"^2)`, y = log(1 +u2)
If x = t.logt, y = tt, then show that `("d"y)/("d"x)` = tt
Find `("d"y)/("d"x)`, if y = (log x)x + (x)logx
Find `("d"y)/("d"x)`, if y = `x^(x^x)`
If xa .yb = `(x + y)^((a + b))`, then show that `("d"y)/("d"x) = y/x`
Find `("d"y)/("d"x)`, if y = x(x) + 20(x)
Solution: Let y = x(x) + 20(x)
Let u = `x^square` and v = `square^x`
∴ y = u + v
Diff. w.r.to x, we get
`("d"y)/("d"x) = square/("d"x) + "dv"/square` .....(i)
Now, u = xx
Taking log on both sides, we get
log u = x × log x
Diff. w.r.to x,
`1/"u"*"du"/("d"x) = x xx 1/square + log x xx square`
∴ `"du"/("d"x)` = u(1 + log x)
∴ `"du"/("d"x) = x^x (1 + square)` .....(ii)
Now, v = 20x
Diff.w.r.to x, we get
`"dv"/("d"x") = 20^square*log(20)` .....(iii)
Substituting equations (ii) and (iii) in equation (i), we get
`("d"y)/("d"x)` = xx(1 + log x) + 20x.log(20)
Solve the following differential equations:
x2ydx – (x3 – y3)dy = 0
If y = x . log x then `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+y)`
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))`
